The character, functions, and styles of instant messaging in the workplace Current perceptions of Instant Messaging (IM) use are based primarily on self-report studies. We logged thousands of (mostly) workplace IM conversations and evaluated their conversational characteristics and functions. Contrary to prior research, we found that the primary use of workplace IM was for complex work discussions. Only 28% of conversations were simple, single-purpose interactions and only 31% were about scheduling or coordination. Moreover, people rarely switched from IM to another medium when the conversation got complex. We found evidence of two distinct styles of use. Heavy IM users and frequent IM partners mainly used it to work together: to discuss a broad range of topics via many fastpaced interactions per day, each with many short turns and much threading and multitasking. Light users and infrequent pairs mainly used IM to coordinate: for scheduling, via fewer conversations per day that were shorter, slower-paced with less threading and multitasking. Informal face-to-face (FTF) communication has been shown to serve many important functions in organizations, including complex coordination, problem solving, and social learning [9, 10, 11, 21] . Early attempts to build tools to support informal communication focused on audio and video environments [1, 4, 7, 19] . However, these attempts have not been widely adopted for several reasons, including the lack of support for core user tasks, cost, privacy concerns, and implementation difficulties [1, 9, 10, 20] .. Instant Messaging (IM), in contrast, has become of great interest to the CSCW community because it is a tool that successfully supports informal communication [5, 6, 13, 14] . Nardi et al. [14] , for example, reported cases where IM was preferred to informal FTF conversation because it is less intrusive and allows multitasking. Furthermore, IM has a huge base of users. Market reports indicate that over 140M people worldwide used IM at the end of 2000 [15] . In addition, IM is used by multiple populations for different purposes: It has been widely adopted by teenagers for socializing, and by adults for both social and work purposes [5, 14] . This suggests that IM merits detailed study. A better understanding of the properties of IM that enable it to support informal communication would help in the design of other novel technologies for supporting informal communication.. Most of our initial understanding of the use of instant messaging comes from self-reports, primarily interview studies [3, 5, 6, 13, 14] or marketing surveys [12, 15, 16] . While helpful for getting a sense of IM practices, these studies usually have been based on relatively small sets of users and little direct observation of instant messaging activity. We were in the fortunate position of being able to collect a large sample of direct observations: over 21,000 IM conversations by 437 users. This should enable us to provide a more accurate picture of IM usage characteristics. We also evaluated these IM conversations qualitatively to refine our understanding of IM functions. We begin by summarizing previous findings. efficient for brief interactions, but when discussion becomes complicated, people often find themselves abandoning the chat and picking up the phone." Second, users switch from IM to another media when participants initiate an IM conversation to arrange an impromptu phone or FTF interaction [13] . In either case, the implication is that IM has limitations for anything more complex than simple and brief interactions.. Finally, multitasking is thought to be prevalent in IM. Several studies note that a major benefit of IM is that conversations can take place while carrying out other activities. Nardi et al. [14] , for example, report that users liked that they could respond to quick IM questions from coworkers while engaged in another task, such as talking on the telephone, or processing documents or email. In other cases, IM was deliberately used to set up a parallel communication channel, e.g., to have a private side conversation during an audio conference. Descriptions of teenagers' use of IM also highlight multitasking, reporting how they carry on multiple simultaneous conversations while surfing the web, answering email, watching TV, or talking on the phone [5] .. Functions. In their study of IM usage in the workplace, Nardi et al. [14] interviewed 20 workplace users and concluded that IM is used primarily for four functions, variations of which are frequently mentioned in other research [3, 5, 6, 12, 13, 15, 16] . These functions include (1) quick questions and clarifications, (2) coordination and scheduling work tasks, (3) coordinating impromptu social meetings, and (4) keeping in touch with friends and family.. The first category, quick questions and clarifications, is most commonly mentioned in other reports. IM is reported to be highly effective for asking quick questions of coworkers, who can respond rapidly without the overhead of telephone or FTF interaction. For example, IDC reports, "Users see IM as a medium for quick, semi-permanent 'flashes' that beg a near-immediate response" [12] .. Other sources point to the role of IM in scheduling meetings or arranging impromptu discussions. IM is reported to be valuable in allowing remote coworkers to set up impromptu phone and FTF conversations [14] . Colleagues who share a physical environment can hold impromptu conversations when they encounter each other [9, 10, 21] . IM provides information about the availability of remote coworkers, enabling similar opportunistic conversations. Milewski & Smith [13] found that a team of researchers frequently used IM to coordinate impromptu phone calls among members of the group. Nardi et al.'s [14] third and fourth categories focus on the social uses of IM, which are echoed in other reports. IM is used to keep in touch with friends and colleagues and to arrange impromptu social meetings. The perception that IM is used primarily for this purpose has led employers to be circumspect about sanctioning the official use of IM at work. One market survey reported, "'Fear of losing employee productivity' was the greatest concern of businesses in regards to instant messaging" [15] . Another indicated that IM is used for "non-business chatting with colleagues, and this fact made even current users feel that IM was a 'less serious' business tool than email" [12] . These findings suggest the need to re-examine certain beliefs about workplace IM use. Prior research on the functions of IM has emphasized its use for rapid singlepurpose exchanges, scheduling, and socializing. Our analysis suggests that these reports have over-emphasized those functions and greatly under-reported its use for extended work discussions, at least among workplace users. We also found that workplace IMs only occasionally turned to personal matters, and few were exclusively personal.. Previous research on IM character suggests that IM conversations are quick, and that multitasking and media switching are prevalent. We found that IM conversations were indeed short, lasting about 4½ minutes, but perhaps longer than expected, and comparable to other impromptu conversations, i.e. via FTF, phone, or desktop videoconferencing. We found that media switching was not especially common (16% of conversations) and very rarely occurred when the conversation became too complex (3%). Instead, when participants did switch media, they used IM deliberately to set up FTF or phone interactions or to call together participants of a meeting. People did frequently multitask while using IM (85% of conversations), as is often reported, but only about 23% of users carried on multiple simultaneous IMs and not that often (10%).. We discovered two styles of use, which we call working together and coordinating. Those who work together use IM for a range of collaborative activities. They have multipurpose discussions, sometimes for scheduling, but more often covering a range of complex work (and sometimes personal) topics. Their conversations are more intense: with many short messages in a short period of time, often threading their messages. They are more likely to take interruptions and less inclined to close their conversations. Furthermore, the intensity of these interactions makes them different from the slow-paced, intermittent style of use mentioned in other studies [5, 14] . Heavy IMers and pairs who interact frequently tend to use IM to work together, and therefore, more IM conversations are of this style.. Those who coordinate have short, single-purpose conversations, often to schedule interactions in another medium. Their conversations are relatively slow-paced: with fewer, longer turns with a minimum of threading. They multitask less often than those who work together, but still do so frequently. They are less likely to interrupt their conversations and are more likely to formally end them. Light IM users and pairs who interact infrequently are most likely to use IM to coordinate, and so fewer conversations overall are of this style.. How can we explain the discrepancies between our findings and those of prior studies? We believe the differences can be explained by three factors. First, some prior studies explored social IM use, primarily among teenagers, which is likely to be different from adults' workplace IM use. Second, although we found that most conversations were of the working together style, more people used the coordination style, so interviews of small numbers of workers may uncover more coordination-style attributes. Third, in self-report studies, people tend to focus on salient, novel behaviors (e.g., bypassing rounds of email to quickly resolve issues, having many simultaneous conversations), taking for granted the ordinary ones (e.g. carrying out work). Content analyses based on logs, on the other hand, can't capture users' intentions or non-computer-based events (e.g. multitasking without leaving the IM window).. We note two caveats. First, while our quantitative results are based on a large data set, our content claims come from a much smaller and more homogenous population. Second, certain results regarding the character of IM may have been affected by Hubbub's unique sound communication and enhanced awareness features, and so may vary from other IM products.. One design implication of these results is that, while it might help to make media switching easier by integrating IM with the phone, users might make use of such a feature less often than expected. People seem to be very effective at discussing complex work topics using just text. And since all users often multitask while IMing, it would be a mistake to tightly integrate IM with certain applications and make it difficult to move to others.. Our results also suggest that the characteristics of heavy IM use -multiple, brief, intermittent interactions per day with minimal closings -mirror the nature of impromptu pairwise interactions in other media [9, 10, 21] . This finding reinforces the notion that these are key characteristics of lightweight, unplanned interactions. Other tools intended to support it must be designed to support those characteristics.. Overall, these results help explain why IM is often used for informal workplace communication, and why it is sometimes preferred to FTF communication [14] . IM supports a broad range of uses: not only rapid, singlepurpose interactions, but also complex work activities.

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A Scalable Formulation of Probabilistic Linear Discriminant Analysis: Applied to Face Recognition Abstract-In this paper, we present a scalable and exact solution for probabilistic linear discriminant analysis (PLDA). PLDA is a probabilistic model that has been shown to provide state-of-the-art performance for both face and speaker recognition. However, it has one major drawback: At training time estimating the latent variables requires the inversion and storage of a matrix whose size grows quadratically with the number of samples for the identity (class). To date, two approaches have been taken to deal with this problem, to 1) use an exact solution that calculates this large matrix and is obviously not scalable with the number of samples or 2) derive a variational approximation to the problem. We present a scalable derivation which is theoretically equivalent to the previous nonscalable solution and thus obviates the need for a variational approximation. Experimentally, we demonstrate the efficacy of our approach in two ways. First, on labeled faces in the wild, we illustrate the equivalence of our scalable implementation with previously published work. Second, on the large Multi-PIE database, we illustrate the gain in performance when using more training samples per identity (class), which is made possible by the proposed scalable formulation of PLDA. IN recent years, a technique known as probabilistic linear discriminant analysis (PLDA) has been proposed [1] for face recognition. This probabilistic technique has since been applied to both face [2] and speaker recognition [3] and achieved state-of-theart performance in both fields.. Despite PLDA's state-of-the-art performance in multiple domains and for multiple tasks, it has a major limiting factor for its application to large datasets. The calculation of the posteriors, for training the model, implies the inversion of a matrix whose size grows quadratically with the number of samples per class, J i . In [3] , a variational approximation was proposed to address this issue. However, the quality of such an approximation is subject to the validity of the questionable assumption (see [3, Section 3] ) that the posterior variables are independent. A similar problem occurs when calculating the likelihood. For this, Kenny [3] proposed a further approximation by using a lower bound of the likelihood and noting that a change of variables could be performed to diagonalize the covariance matrix. To do this efficiently, it was noted that the matrix needed to perform the change of variable could be computed offline. However, it had to be loaded and used whenever the likelihood was calculated.. In this paper, we show that, for PLDA with a Gaussian prior, the calculation of the posteriors (for training) and the calculation of the likelihood have exact closed form solutions that are scalable. This exact closed form and scalable solution, which has thus far not been presented anywhere else, obviates the need for the approximations proposed by Kenny [3] and is the main contribution of this paper. This contribution provides three significant advantages over prior work. First, we provide a scalable way to derive the posteriors and thus a scalable way to perform training that does not involve any approximations. Second, we detail an exact and scalable way to calculate the joint probability of the samples which has never been presented before, neither in [2] nor [3] . Third, and finally, we show that enrollment of a client (storing the information for a model) reduces to calculating a single low-dimensional feature vector rather than retaining multiple high-dimensional feature vectors. This further improves the efficiency and scalability of the model.. We briefly present PLDA and the origin of the problems for scalability for both training and computing the likelihood in Section 2. In Section 3, we describe how, by introducing a welldefined change of variable, it is possible to derive exact closed form solutions for the posteriors and the likelihood that are scalable. Section 4 discusses the complexity of previous and proposed approaches. Finally, in Section 5, we demonstrate experimentally that, for the task of face authentication, it is advantageous to train the PLDA system with many samples per class, which is only made possible by the proposed scalable formulation. We present results on Multi-PIE by quoting the half total error rate (HTER), similar to the results produced for BANCA [14] . The HTER is a performance measure that obtains a threshold at the equal error rate point on an independent development set that is then applied to an evaluation set. The HTER is then obtained by taking the average of the false acceptance rate and the false rejection rate on the evaluation set at this threshold .. The results for PLDA and the three reference systems can be found in Table 3 . These results make use of the full training set, 9,785 images, where there were at most 76 images per identity and as few as 19 images per identity. It can be seen from these results that PLDA consistently outperforms every other system.. Using the previous result, we took the optimal hyperparameters of PLDA, D F ¼ 128 and D G ¼ 64, and varied the number of training images per identity to show the impact on performance. 8 We varied the maximum number of training samples per identity from 2 to 76 and plotted the relative size of the matrices needed to compute the latent variables (on a log-scale) versus the number of training samples; the results are plotted in Fig. 2 . The matrices used to compute the latent variables for 1) the scalable derivation were F F F F T S S S S, ðI I I I DG þ G G G G T AE À1 G G G GÞ À1 , and ðI I I I DF þ J i F F F F T S S S SF F F F Þ À1 and 2) the nonscalable derivation was ðĨ I I I þÃ A A A TAEÀ1Ã A A AÞ À1 .. In Fig. 2 , we also provide a plot of the HTER versus the number of training samples. It can be seen that, for these experiments, adding more training samples always improves performance. This clearly shows the applicability of a scalable form of PLDA because, as the number of training samples increases, it quickly becomes infeasible to use a nonscalable derivation. Accuracy is presented in terms of mean classification accuracy and the standard error of the mean [5] . Fig. 1 . Three example images for one identity in mutli-PIE along with a corresponding bounding box for cropping the face image in green. 6. These annotations are available at: www.idiap.ch/resource/biometric. Also, there are 20 images per session, but two of these are almost exactly the same and so we only retain one of them, resulting in 19 images per session.. 7. We have an overlap margin of 4 pixels between consecutive blocks. 8. For the optimal parameters, the PLDA system took approximately 35 minutes to train using 9,785 images and 45 minutes to produce the scores (including enrollment) for the 311,296 development probes. These experiments were run on an Intel Quad Core CPU 2.50 GHz computer using a C++ implementation without multithreading.. We have presented a novel and scalable derivation for training PLDA. This derivation is theoretically equivalent to the previous nonscalable solution [4] and so obviates the need for a variational approximation [3] . Aside from the theoretical proof, we further demonstrate the efficacy of this technique by performing experiments on two well-known face databases. First, on LFW we illustrate the equivalence of our model with that of [2] , which achieves state-of-the-art performance on several face recognition problems. Second, on the large Multi-PIE database, we illustrate the gain in performance when using more training samples per identity (class) and so demonstrate the need for a scalable solution. Our second contribution has been to present a novel and scalable derivation for computing the likelihood of PLDA, which we have used in all of our experiments. Finally, we show that enrollment of a client (storing the information for a model) reduces to calculating a single low-dimensional feature vector rather than retaining multiple high-dimensional feature vectors. Fig. 2 . We plot the HTER achieved using the PLDA system on the Multi-PIE database, showing that the error rate decreases as we use more samples per identity. Matrix size is also plotted to contrast the corresponding memory usage of the nonscalable and scalable solutions in terms of the log number of elements in the matrices used to compute the latent variables. The PLDA model proposed by Prince and Elder [1] has been shown to provide state-of-the-art performance for both face recognition [4] , [2] and speaker recognition [3] . However, the model has one major problem. It cannot be easily applied to large datasets. This was highlighted by Kenny [3] , for the task of speaker recognition.. The PLDA model [1] assumes that the jth image of the ith client can be described by the following process:. In this process, the input signal x x x x i;j , of dimensionality D x , is considered to consist of: 1) the identity part given by þ F F F F h h h h i and 2) the noise component given by G G G Gw w w w i;j þ i;j . The matrices F F F F and G G G G are subspaces that contain the bases for the between-class variation and within-class variation respectively, these subspaces are of size ðD x ; D F Þ and ðD x ; D G Þ, respectively. Correspondingly, h h h h i and w w w w i;j represent the position in these subspaces for x x x x i;j and are of size D F and D G , respectively. Finally, the residual i;j , is defined to be Gaussian with zero mean and diagonal covariance AE.. The process above can be described in terms of a conditional probability P rðx x x x i;j jh h h h i ; w w w w i;j ; ÂÞ ¼ N ½ þ F F F F h h h h i þ G G G Gw w w w i;j ; AE;. and prior probabilities (I I I I being the identity matrix). P r ðh h h h i Þ ¼ N ½0; I I I I; ð3Þ P r ðw w w w i;j Þ ¼ N ½0; I I I I;. where the parameters of the model are Â ¼ ½ ; F F F F ; G G G G; AE.. Equations (3) and (4) define the priors on the latent variables, h h h h i and w w w w i;j , to be Gaussian. The equations above can be written in a more compact form by setting A A A A ¼ ½F F F F ; G G G G and. This would give us x x x x i;j ¼ þ A A A Ay y y y i;j þ i;j ; ð6Þ and P r ðx x x x i;j jy y y y i;j ; ÂÞ ¼ N ½ þ A A A Ay y y y i;j ; AE; ð7Þ P r ðy y y y i;j Þ ¼ N ½0; I I I I:. We can extend the above formulation to handle multiple observations. For instance, if we are given J i ¼ 2 observations for identity i we would setÃ. Consequently, we would write thatx x x x i ¼ ½ . the tilde symbol~indicating that the size of a variable (or a matrix) depends on the number of samples J i for the class i. This notation makes it explicit that we tie all of the J i observations for identity i to have the same latent identity variable h h h h i but to have different latent session, or noise, variables w w w w i;j ; with such a formulation we would drop the reference to , the mean of the data, in the Gaussian as it has already been subtracted from the samples in (11) .. For the general case of a class i with J i samples and keeping the same notation, the model could be rewritteñ. There are two main tasks that we wish to accomplish with this probabilistic model. The first is to train the model and this is achieved using an expectation-maximization (EM) algorithm. The second is to use the trained model to perform recognition and it was shown [1] that central to this problem is to calculate the likelihood that a set of observations, ½x x x x i;1 ; x x x x i;2 ; . . . ; x x x x i;Ji , share the same latent identity variable h h h h i . Below we provide some more details on each of these tasks.

O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A Fixed-Parameter Tractability Result for Multicommodity Demand Flow in Trees We study an NP-hard (and MaxSNP-hard) problem in trees-Multicommodity Demand Flow-dealing with demand flows between pairs of nodes and trying to maximize the value of the routed flows. This problem has been intensively studied for trees as well as for general graphs mainly from the viewpoint of polynomialtime approximation algorithms. By way of contrast, we provide an exact dynamic programming algorithm for this problem that works well whenever some natural problem parameter is small, a reasonable assumption in several applications. More specifically, we prove fixed-parameter tractability with respect to the maximum number of the input flows at any tree node. As a rule, most hard problems on graphs turn easy when restricted to trees. There are, however, notable exceptions of important graph problems that remain hard even in trees. A well-known example is the Bandwidth Minimization problem restricted to trees of maximum degree three where it still remains NP-complete [10] . In this paper, we deal with another well-studied graph problem that remains NP-complete when restricted to trees. The problem is Multicommodity Demand Flow in Trees (MDFT), where the tree edges have limited capacities, each demand (i.e., flow) between two nodes has a certain value and each successfully routed demand brings a certain profit; the goal is to maximize the profit by routing as many and as good flows as possible. We refer to Sect. 2 for more details and formal definitions. It follows from the work of Garg, Vazirani, and Yannakakis [8] that this problem is NP-complete and MaxSNP-hard. Moreover, constant-factor polynomial-time approximation algorithms are known [4, 8] . By way of contrast, we investigate the exact solvability of this problem by fixed-parameter algorithms.. Exact algorithms for NP-hard problems have become a flourishing field of research [6, 9, 12, 13] . In particular, fixed-parameter algorithms are now often seen as valuable alternatives to approximation algorithms. The basic idea is to try to derive exact algorithms with a combinatorial explosion (i.e., exponential running time factor) that can be confined to some (hopefully small) problem parameters. Formally, a parameterized problem is fixed-parameter tractable if it has a solving algorithm that runs in O(f (k) · n c ) time, where f is an arbitrary computable function only depending on k, k is the input parameter, n is the problem size, and c is a constant [6, 12] (see [5, 7, 11] for recent surveys). Meanwhile, many successful examples of fixed-parameter algorithms for hard problems exist. Here, we contribute one further example of this sort, complementing previous work on approximation and fixed-parameter algorithms. More precisely, we show that MDFT is fixed-parameter tractable with respect to the parameter "maximum number of the input flows running through or to any node of the input tree network." Interestingly, as further discussed in the concluding section, there is no hope for fixed-parameter tractability for MDFT when replacing in the parameter the term "node" by "edge". Our new fixed-parameter algorithm for MDFT is conceptually simple enough to allow easy implementation and, also because of that, may appear as profitable alternative to existing approximation algorithms. Employing dynamic programming, we obtained a fixed-parameter tractability result for Multicommodity Demand Flow in Trees. Our result complements previous work mainly dealing with the polynomial-time approximability of this and related problems. We claim that our exact algorithm is conceptually simple enough to be valuable in practice. Clearly, the immediate challenge is to significantly improve the exponential time bound of our algorithm.. Note that the parameter in our fixed-parameter tractability result relates to the maximum number of flows passing through any node of the input tree. The natural question arises what happens when we replace "node" by "edge". Somewhat surprisingly, a simple adaption of an NP-completeness proof of Garg et al. [8, Theorem 4.2] shows that MDFT is NP-complete even when there are at most six demand flows passing through an edge. Hence there is no hope for fixed-parameter tractability with respect to the parameter "maximum number of demand flows passing through any edge of the tree network". Finally, as pointed out by an anonymous referee, it seems worth studying the complexity of MDFT when parameterized by the number of the demand flows through any node in a solution instead of the number of demand flows through any node in the input (as we did here). We leave it as an open question to investigate the parameterized complexity for this modified parameterization.

O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Short collusion-secure fingerprint codes against three pirates In this article, we propose a new construction of probabilistic collusion-secure fingerprint codes against up to three pirates and give a theoretical security evaluation. Our pirate tracing algorithm combines a scoring method analogous to Tardos codes (J. ACM, 2008) with an extension of parent search techniques of some preceding 2-secure codes. Numerical examples show that our code lengths are significantly shorter than (about 30% to 40% of) the shortest known c-secure codes by Nuida et al. (Des. Codes Cryptogr., 2009) with c = 3. Some preliminary proposal for improving efficiency of our tracing algorithm is also given. In this article, we proposed a new construction of probabilistic 3-secure codes and presented a theoretical evaluation of their error probabilities. A characteristic of our tracing algorithm is to make use of both score comparison and search of the triples of "parents" for a given pirated fingerprint word. Some numerical examples showed that code lengths of our proposed codes are significantly shorter than the previous provably secure 3-secure codes. Moreover, for the sake of improving efficiency of our tracing algorithm, we also proposed an implementation method for the algorithm, which seems indeed more efficient for an average case than the naive implementation. A detailed evaluation of the proposed implementation method will be a future research topic.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A contribution to vision-based autonomous helicopter flight in urban environments A navigation strategy that exploits the optic flow and inertial information to continuously avoid collisions with both lateral and frontal obstacles has been used to control a simulated helicopter flying autonomously in a textured urban environment. Experimental results demonstrate that the corresponding controller generates cautious behavior, whereby the helicopter tends to stay in the middle of narrow corridors, while its forward velocity is automatically reduced when the obstacle density increases. When confronted with a frontal obstacle, the controller is also able to generate a tight U-turn that ensures the UAV's survival. The paper provides comparisons with related work, and discusses the applicability of the approach to real platforms. When the external world is projected onto the image plane of a camera, the movements of each point in this plane define the so-called motion field, from which information about the self-motion of the camera or about the structure of the scene can be inferred. When such movements are sampled, by means of a video stream for instance, the apparent motion of pixels in the image constitutes the optic flow, which is a convenient approximation of the motion field if the intensity of each pixel is preserved from one frame to the next. This is why, to compute the optic flow in this work, the hue of each pixel (i, j) is used to evaluate its intensity value I(i, j), because this type of data is not very sensitive to changes in light intensity.. Several varieties of algorithm can be used to compute optic flow [3] . Differential methods [21, 26] call upon spatio-temporal intensity derivatives. Correlation approaches [1] rely on feature matching. Frequency-based methods [16] use velocity-tuned filters in the Fourier domain. In this work, correlation techniques have been preferred because they are known to be robust and because experience demonstrates that they are accurate enough to make efficient control possible. This work describes how a bio-inspired vision system, which monitors optic flow in real time, can be used to control the flight of a simulated autonomous helicopter in an unknown urban environment. The corresponding controller takes inertial information into account to separate the rotational and lateral components of the optic flow. This implementation generates cautious behavior, whereby the helicopter tends to stay in the middle of narrow corridors, while its forward velocity is automatically reduced when the obstacle density increases. Moreover, when heading into a frontal obstacle, the controller is able to generate a tight U-turn that ensures the UAV's survival.. When compared to related works, the simulations described here prove in some ways more realistic than other approaches where real helicopters were used, but with prepared environments and/or freedom restrictions. Moreover, it seems that no convincing reports of the successful implementation of obstacle-avoidance mechanisms on an autonomous real helicopter have yet been published. This will be the objective of our future work. The system described herein calls upon an on-line monitoring of the optic flow and makes safe and adaptive helicopter flights possible, even in cluttered urban environments. This is partly due to the use of the real-time quantized algorithm, which calls upon simple computational principles and proves to be less time-consuming and more robust than other approaches we tried to implement. This is also due to the compensation of the rotational component of the optic flow, which allows higher speeds and smoother trajectories than the implementation of any zig-zag strategy. It turns out that the latter result is mostly due to the right tuning of the η target parameter. Indeed, increasing this value too much would lead to some crashes during U-turns because, V target x being set to zero, the PID modules on V x and ψ would not be efficient enough to prevent the helicopter from leaving its flight envelope 6 .. In its current stage of development, the control system described here is rather simple. Being inspired by behavior-based robotics [2] and the work of Gibson [19, 20] , it tends to minimize the information acquisition and processing necessary to control the implemented behaviors. In particular, it does not require managing the kind of internal representations that would be necessary for cognitive mapping, self-localisation and trajectory planning, for instance [15, 27] . However, with the help of an additional GPS module, it could easily be endowed with goal-directed navigation capacities, as demonstrated by the work of Duchon [11] . The solution would be to add a bias γ to Eq. 6, which would become:. where:. Variable β designates the bearing of the goal with respect to the direction of the helicopter, and may be deduced from the GPS information. To prevent the helicopter from turning instantaneously toward the goal, only a given percentage perc of β is used to modify the current direction. Likewise, to avoid aiming directly at a goal that is on the other side of a wall, the value of Σ, i.e., the sum of the norms of the detected motions, is taken into account.. As a is an appropriately scaled constant, the term 1 − Σ a is necessary to balance obstacle-avoidance reflexes and goal-directed behaviors. In dangerous situations, the helicopter will be able to turn away from the goal because, when Σ increases, γ decreases.. Several other research efforts have aimed at implementing biomimetic visual controllers on simulated or real UAVs. In particular, Neumann and Bülthoff [32] [33] [34] designed a simulated UAV which was able to stabilize its attitude and avoid obstacles thanks to optic flow computation in a spherical field of view using Elementary Motion Detectors (EMD) that are inspired by the housefly's visual system. However, the corresponding simulation, unlike ours, does not take inertia into account, which is acceptable for very small platforms with a low Reynolds number, such as insects, but is not realistic for larger aircrafts.. Franceschini et al. [18, 28, 39, 17, 31 ] also apply EMDs inspired by the housefly's to control real flying engines. However, the environments they use are equipped with black and white stripes perpendicular to the direction of motion detection, thus affording high contrasts and reliable estimates of optic flow. Moreover, the control laws they designed concern one degree of freedom only, as the corresponding engines are tethered to a rotating support and can only change their altitude. Reiser and Dickinson's approach [35] is very similar and implements EMD-based mechanisms for saccade initiation and visually controlled translational velocity in a gantry fly moving in a highly-contrasted experimental setup. As of today our system has been tested in simulation only, but it deals with more degrees of freedom and more challenging environments than those just quoted.. In a general review of biomimetic visual sensing applied to flight control, Barrows et al. [4] report that they used a biomimetic visual sensing approach to control the altitude of a real helicopter. They also mention that they developed an autopilot fusing optic flow measurement and inertial information to detect nearby objects. However, too few details are provided to make a comparison with the results presented here possible. Nevertheless, this review strongly suggests that the technology advocated here has already been successfully implemented on real flying platforms. Subsequent work will be aimed at filling the reality gap and at implementing this control system on a Concept 60 SR II engine, for which several characteristics of the simulator were specifically tailored. Moreover, great care has been taken to capitalize on simulated sensors that are easily available off the shelf. In a first stage, the controller will be tested with images acquired during real helicopter flights, as done in [22] , to check the efficiency of the optic flow processing and to assess whether on-board vibration problems need to be solved. Later work will be dedicated to coping with air turbulences, which are notoriously difficult to simulate realistically when urban environments are concerned.

O O O O O B O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


An adaptive updating protocol for reducing moving object database workload In the last decade, spatio-temporal database research focuses on the design of effective and efficient indexing structures in support of location-based queries such as predictive range queries and nearest neighbor queries. While a variety of indexing techniques have been proposed to accelerate the processing of updates and queries, not much attention has been paid to the updating protocol, which is another important factor affecting the system performance. In this paper, we propose a generic and adaptive updating protocol for moving object databases with less number of updates between objects and the database server, thereby reducing the overall workload of the system. In contrast to the approach adopted by most conventional moving object database systems where the exact locations and velocities last disclosed are used to predict their motions, we propose the concept of Spatio-temporal safe region to approximate possible future locations. Spatio-temporal safe regions provide larger space of tolerance for moving objects, freeing them from location and velocity updates as long as the errors remain predictable in the database. To answer predictive queries accurately, the server is allowed to probe the latest status of objects when their safe regions are inadequate in returning the exact query results. Spatio-temporal safe regions are calculated and optimized by the database server with two contradictory objectives: reducing update workload while guaranteeing query S. Chen (B) · B. C. Ooi School of Computing, National University of Singapore, Singapore, Singapore e-mail: chensu@comp.nus.edu.sg B. C. Ooi e-mail: ooibc@comp.nus.edu.sg Z. Zhang Advanced Digital Sciences Center, Illinois at Singapore Pte, Singapore, Singapore e-mail: zhenjie@adsc.com.sg accuracy and efficiency. To achieve this, we propose a cost model that estimates the composition of active and passive updates based on historical motion records and query distribution. More system performance improvements can be obtained by cutting more updates from the clients, when the users of system are comfortable with incomplete but accuracy bounded query results. We have conducted extensive experiments to evaluate our proposal on a variety of popular indexing structures. The results confirm the viability, robustness, accuracy and efficiency of our proposed protocol. Spatio-temporal databases, especially Moving Object Databases (MOD), are well studied by the database community to support a variety of queries for location-based services. Two typical example queries are "Q1: Which are the vehicles remaining in Central Park now?" or "Q2: Who will be the policeman closest to City Hall after 5 minutes?". These queries can be formalized with range query and nearest neighbor query on current and future locations of objects in a two-dimensional (2D) space. In order to answer such queries, a moving object database keeps tracks of all objects in the system by receiving occasional location disclosures from objects. Figure 1 shows a typical architecture of a moving object management system. While most of the existing studies on moving object databases focus on enhancing indexing and query processing efficiency, less effort has been made to address the issue on the updating mechanism/protocol, which is yet another crucial factor affecting the system workload and performance even more. Considering the limited room of technical advances on indexing structures and query optimization, it is now important to reconsider the design of the updating protocol. This paper makes the first attempt on a systematic investigation on this possibility. In particular, we propose a new adaptive updating protocol, called STSR-based updating Protocol, which reduces the object updating frequency by maintaining only relaxed motions instead of exact ones in the database. The design of the protocol is on the basis of a careful analysis on the advantages and disadvantages of the existing protocols. In summary, the proposed STSR-based updating protocol achieves reasonably good query precision and outperforms the STP updating method with regard to the query recall. In addition, the STSR-based updating protocol can effectively reduce the updating workload when query predictive time is in a reasonable range. Enabling approximate query processing can further reduce the updating workload to a large extent while still provide a guarantee on the quality of query results. Among all the STSR strategies and indexing structures, the 'BX-G', i.e., the B x -tree with the global dynamic STSR strategy, achieves the best performance with respect to the computational and updating workload in general. In this paper, we propose a generic updating protocol for moving object databases that is independent of the underlying index structure. By utilizing the concept of spatio-temporal safe region (STSR), objects actively send motion updates including their locations and velocities to the database server only when the prediction error of their current movement is no longer bounded. To guarantee the accuracy of predictive query answers, the database server asks objects for their latest locations and velocities, if they are potential answers of the query. To minimize the updating workload, we present a cost model that analyzes the approximate updating cost, depending on the most recent update records maintained in the system. Based on the cost model, an effective optimization technique is designed to construct STSRs that minimize the expected updating cost. To further cutting the cost, the STSR-based updating protocol is extended by allowing incomplete query answers with bounded accuracy. We carefully evaluate three different implementation strategies, including static STSR, dynamic global STSR and dynamic personal STSR. Experiments on the TPR-tree and the B xtree show that our proposed protocol significantly reduces the updating cost while achieving high accuracy of predictive query answers. In this section, we discuss the experimental results on the basis of the settings introduced in previous section. Specifically, Sect. 8.2.1 focuses on the effectiveness of STSR-based protocol without using any index. Section 8.2.2 compares our proposal against existing updating protocols. Then, in Sect. 8.2.3, we show the results of the performance of approximate query processing. Section 8.2.4 presents results when different implementation strategies are applied on different index structures. In this section, we review the existing studies on indexing structures for predictive queries on moving object database (Sect. 2.1), as well as query processing techniques on continuous spatial queries (Sect. 2.2).

O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O


Survey on Model-based Manipulation Planning of Deformable Objects A systematic overview on the subject of model-based manipulation planning of deformable objects is presented. Existing modelling techniques of volumetric, planar and linear deformable objects are described, emphasizing the different types of deformation. Planning strategies are categorized according to the type of manipulation goal: path planning, folding/unfolding, topology modifications and assembly. Most current contributions fit naturally into these categories, and thus the presented algorithms constitute an adequate basis for future developments. Manipulation planning differs from standard motion planning in that the focus is not on the robot and its displacements but rather on the object(s) to be manipulated. Manipulation of rigid objects consists basically in changing their pose (position and orientation), while avoiding collisions, in the context of pick-and-place or assembly tasks. Realistic instances of the problem take also constraints on the stability of the grasp and of the placement of the object into account (see [1] for a small survey on the subject). When deformable objects are involved, manipulation will in most cases also affect their shape, with geometrical or topological changes. This behavior has to be considered in the whole planning process.. Most existing robotic systems that handle deformable objects rely heavily on a sensor-based control scheme. Many of them are ad-hoc algorithms, which lack generality [2] . Moreover, flexibility of such systems is also poor, as they implement fixed strategies. Sensorial feedback may be necessary in real implementations to overcome uncertainties in the model, which will probably arise except in very controlled environments. Furthermore, sensorial information is also needed in the automatic acquisition of behavior models of deformable objects under manipulation (i.e., machine learning of manipulation), a little explored issue. A collection of control-related articles can be found in [3] .. Planning chooses and/or instantiates a sequence of actions from a given repertoire. This choice is not only conditioned by the intended sequence of states (in this case, configurations of the manipulated object) but also by the constraints that each state poses on the possible actions. Here, internal and external constraints have to be considered, as well as feasibility (hard) and optimization (soft) constraints. Constraints allow to narrow the search space of actions to consider, and to introduce criteria for evaluating different choices.. The present work concentrates on model-based off-line manipulation planning, which is based on geometrical (and to some extent also physical) descriptions of the object to be manipulated and its environment. We also assume that the wealth of possible sequences of elementary motions or actions makes it necessary to devise the manipulation plans automatically. Furthermore, some kind of prehensile grasping is involved in manipulation (see [4] for nonprehensile manipulation). In the works referenced in our survey, simplified models of grasping are adopted, in the form of manipulation constraints that define the location of grasps on the object and tangents of its surface at these points, and assuming that the forces exerted by the fingers ensure the intended deformations without damaging the object.. Deformations depend on the material properties of the objects, on their initial shape and dimensions, and also on the localization, direction, intensity, duration and frequency of the applied forces. As for manipulation planning, there are two features that characterize object deformations: reversibility and direction/extension of the shape change. The first criterion refers to whether the object recovers completely its original (rest) shape once the external forces have ceased (elastic deformation), or if permanent, stable deformations appear on the body of the object (plastic deformation). A third category of deformations may be considered, as for reversibility, which is applicable to material like cloth or rope. We call them flexible deformations, as they are neither elastic (due to friction and gravity, the object does not recover anything like a "rest shape" once manipulation ends) nor strictly plastic, as they can be altered with very slight effort. Such definition is not a standard one in materials science or deformation theory, but it is intuitive and useful for robotic planning purposes.. Deformations are also characterized by the direction in which they take place, as a result of the direction of the applied forces and moments. Figure 1 displays a schematic view of some basic deformation types for a cylinder. The undeformed cylinder appears in the center of the figure. Arrows stand for the forces and moments exerted on the cylinder, while the cross drawn on it helps to visualize the resulting deformation. At the left, tension, compression and shear, and on the right bending and torsion are exemplified. The suitability of different model types is related to the type of deformation: curves and surfaces are appropriate for elastic deformations, massspring meshes and particle systems for elastic and flexible deformations, and polyarticulated analogues for plastic deformations. As for planning strategies, path planning lies at the lower abstraction level in our categorization, and random sampling methods have been successfully adapted to cope with this problem. There are still variants of these methods to be tested for suitability in our context. The main research challenge consists, however, in efficiently biasing this basic search procedures towards the significative parts of the configuration space, as has been described for the latter three manipulation goal categories. There, plans are generated that prescribe a sequence of motions and actions at a level of certain abstraction, what in [104, 105] is called a qualitative manipulation plan. There are still open research issues as for effective formulations of qualitative plans, like the definition of "discrete" states for flexible material (e.g. straightened, folded, squashed, crumbled, etc.) that has to cope with a high degree of fuzzyness. Kinodynamic planning [116, 117] , on the other hand, operates directly in the space of dynamic models and its use in manipulation planning of deformable objects is still quite unexplored. Possible integration directions between sensorand model-based manipulation, like learning basic manipulation skills or uncertainty handling, also deserve further exploration.. Along this survey, a few specific suggestions on punctual open issues have been done. Besides, other open questions include bimanual manipulation of deformable objects (some pioneering work has been done in [43] ), which is clearly an issue of concern for humanoid robots performing everyday tasks, and dexterous handling of deformable objects, like multifingered manipulation of planar deformable objects using a vision-based control law [118] , or one-handed knot-tying using tactile sensors [119] .

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Geometrical position tolerance assignment in reverse engineering Geometric dimensioning and tolerancing constitutes the dominant approach for design and manufacture of mechanical parts that control inevitable dimensional and geometric deviations within appropriate limits. Position tolerance is a critical geometric tolerance very frequently used in industry. Its designation requires size data in conjunction with appropriate datums and location coordinates for the position. In reverse engineering, where typically relevant engineering information does not exist, conventional, humanbased, trial and error approach for the allocation of positional tolerances requires much effort and time and offers no guarantee for the generation of the best results. This is mainly due to the large number of possible data combinations and the applicable relationships that have to be developed and processed. A methodology that aims towards the systematic solution of this problem in reasonable computing time and provides realistic and industry approved results is presented, demonstrated and discussed in the paper. In manufacturing, deviations from the nominal geometric and dimensional requirements of a mechanical part are expected due to the stochastic nature of the actually achieved accuracy. Geometric dimensioning and tolerancing (GD&T) constitutes the dominant approach for the design and manufacture of mechanical parts that control these inevitable deviations within appropriate limits. In engineering drawings GD&T correlates size, form, orientation and location of the geometric elements of the design model with the design intent, therefore it has a profound impact on the manufacturability, ease of assembly, performance and ultimate cost of the component. High geometrical and dimensional accuracy leads to high quality; however, tight tolerances lead to an exponential increase of the manufacturing cost.. Tolerance assignment is an engineering task strongly based on experimental data, past experience, industrial databases and guidelines. In reverse engineering (RE) tolerancing is much more difficult to be successfully handled. In this case all or almost all of the original component design and manufacturing information is not available and the geometric accuracy specifications for component reconstruction have to be reestablished, one way or another, practically from scratch. RE-tolerancing includes tolerance allocation in terms of the actual functionality of a prototype assembly, mapping of component experimental design modifications, spare part tolerancing for machines that are out of production or need improvements and no drawings are available, damage repair, engineering maintenance, etc. The task requires increased effort, cost and time, whereas the results, usually obtained by trial-and-error, may well not be the best.. Although RE-tolerancing is a very important and frequently met industrial problem, the need for the development of a systematic approach to extract appropriate design specifications that concern the geometric accuracy of a reconstructed component has been only recently pointed out, (Motavalli and Shamsaasef 1996 , Thompson et al. 1999 , Borja et al. 2001 , Va´rady and Martin 2002 , VPERI 2003 . Some of its issues are also addressed by a limited number of research papers, (Werghi et al. 1999 , Kaisarlis et al. 2000 , Werghi et al. 2002 , Kaisarlis et al. 2004 ). This paper further extends the research on this area by focusing on the RE assignment of Position Tolerances, as this type of geometrical tolerance is a widely used one in industry and almost always present in reverse engineering applications. The developed methodology addresses the problem in a systematic, time and cost efficient way, compatible with the current industrial insight. The approach, to the extent of the authors' knowledge, is the first of the kind for this type of RE problems that can be directly implemented within a CAD environment. It can also be considered as a pilot for further research and development in the area of RE tolerancing. The method use and effectiveness are demonstrated through an actual industrial case study. Considering that tolerances in component reconstruction are crucial for component performance and interchangeability, assignment of the appropriate geometrical and dimensional accuracy data in RE is extremely difficult due to the lack of adequate information. This is particularly true for the frequently met position tolerances. The methodology developed and presented in this paper produces, in reasonable time, realistic results for position tolerancing in industrial reverse engineering and can be used both for rotational and prismatic features. The method can be directly integrated into a CAD environment for reverse engineering. Further development is under way in order for the method to include MMC/LMC application to datums, fixed fasteners and position tolerance size not equally distributed between the mating parts.

O B I O O B I O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O


Proximity In Arrangements Of Algebraic Sets Abstract. Let X be an arrangement of n algebraic sets X i in d-space, where the X i are either parametrized or zero-sets of dimension 0 ≤ m i ≤ d − 1. We study a number of decompositions of d-space into connected regions in which the distance-squared function to X has certain invariances. Each region is contained in a single connected component of the complement of the bifurcation set B of the family of distance-squared functions or of certain subsets of B. The decompositions can be used in the following proximity problems: given some point, find the k nearest sets X i in the arrangement, find the nearest point in X, or (assuming that X is compact) find the farthest point in X and hence the smallest enclosing (d − 1)-sphere. We give bounds on the complexity of the decompositions in terms of n, d, and the degrees and dimensions of the algebraic sets X i .

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Hardness results for the center and median string problems under the weighted and unweighted edit distances Given a finite set of strings, the MEDIAN STRING problem consists in finding a string that minimizes the sum of the edit distances to the strings in the set. Approximations of the median string are used in a very broad range of applications where one needs a representative string that summarizes common information to the strings of the set. It is the case in classification, in speech and pattern recognition, and in computational biology. In the latter, MEDIAN STRING is related to the key problem of multiple alignment. In the recent literature, one finds a theorem stating the NP-completeness of the MEDIAN STRING for unbounded alphabets. However, in the above mentioned areas, the alphabet is often finite. Thus, it remains a crucial question whether the MEDIAN STRING problem is NP-complete for bounded and even binary alphabets. In this work, we provide an answer to this question and also give the complexity of the related CENTER STRING problem. Moreover, we study the parameterized complexity of both problems with respect to the number of input strings. In addition, we provide an algorithm to compute an optimal center under a weighted edit distance in polynomial time when the number of input strings is fixed. Given an alphabet Σ, a set W of strings over Σ , and an edit distance between strings, the problem of finding a string over Σ that minimizes the sum of edit distances to the strings of W is called the MEDIAN STRING problem. Alternative terminologies include the GENERALIZED MEDIAN STRING problem [2] , the STAR ALIGNMENT problem [12] , the CONSENSUS ALIGNMENT problem [13] and also the STEINER STRING problem [8] .. The MEDIAN STRING problem is of major significance in several areas of research: pattern recognition, speech recognition and computational biology. Its importance is reflected by the wide use of a polynomial time approximation, the set median string [7] [8] [9] [10] 19, 20] . In this restricted version of the problem, the solution string must be taken in the input set W (it is also termed the "center string" in [8, p. 349] ). One class of applications, encountered in all three areas, looks for a string (or a language) that models the input set of strings. In other words, this string summarizes the information shared by the strings of W . Depending on the application, it then serves as an index for W (in databases and data mining), as a pattern that is searched for in longer texts (in computational biology [8, 22] ) or used for classification purposes (in speech recognition [10] , classification [8] and computational biology [8, 22] ).. In computational biology, computing a median string of a set W is equivalent to solving a MULTIPLE ALIGNMENT problem, which is one of the most important and difficult problems in this area [8] . In practice, MULTIPLE ALIGNMENT may be easier when the evolutionary relationships of the species bearing the sequence are known. The input of the so called TREE ALIGNMENT problem is then a set of strings W and a tree whose leaves are labeled by the strings of W . The objective is to find strings for the internal nodes, such that the sum of edit distances between adjacent strings/nodes over all edges is minimal. A special case of tree of theoretical importance is the star tree: there the computed internal string is a median string [8, 24] . As already mentioned, the median string can serve as consensus of the strings in W , especially if the strings occupy homogeneously the metric space around the median. Unfortunately, in practical applications, the strings in W are not a uniform sample of the evolutionary diversity: some evolutionary families of strings in W are more represented than others. In such cases, minimizing the sum of the edit distances results in a biased alignment and consensus (see [1] for a discussion about this matter). Minimizing the maximum edit distance, i.e., computing a center string, produces solutions that reflect more faithfully the variations in W . For this purpose, Ravi and Kececioglu introduced in 1995 a variant of the TREE ALIGNMENT problem with this objective. It is called the BOTTLENECK TREE ALIGNMENT. When the input tree is a star, the BOTTLENECK TREE ALIGNMENT problem is equivalent to the CENTER STRING problem.. In [2] , it is shown that CENTER STRING and MEDIAN STRING are NP-hard for alphabets of size at least 4 and for unbounded alphabets, respectively. In many practical situations, the alphabet is of fixed constant size. In computational biology, the DNA and protein alphabets are respectively of size 4 and 20. However, other alphabet sizes are also used. Indeed, for some applications, one needs to encode the DNA or protein sequences on a binary alphabet that expresses only a binary property of the molecule, e.g., hydrophoby for proteins or purine-pyrimidine composition for nucleic acids. For instance, it is the case in some protocols to identify similar DNA sequences [27] . The important practical ques-tion is whether CENTER STRING and MEDIAN STRING are NP-hard for finite and even binary alphabets. In the above-mentioned article, these questions remain open [2, p. 48] . These conjectures are solved in this paper. Additionally, an interesting issue concerns the existence of fast exact algorithms when the number of input strings is fixed. We provide an answer to this issue for both CENTER STRING and MEDIAN STRING. In Section 2.1 (see also [21] ), we have shown that CENTER STRING under Levenshtein distance is NP-complete and W[1]-hard with respect to the number of input strings, even for binary alphabet. In Section 3, we generalize these results to any weighted edit distance that satisfies a natural condition. This condition is fulfilled in many applications of computational biology for instance. It remains open to find any particular weighted edit distance (of course, one that does not satisfy our condition) for which CENTER STRING would be polynomial, but this seems improbable.. Concerning MEDIAN STRING, we have shown (Section 2.2) that under the Levenshtein distance it is also NP-complete and W[1]-hard with respect to the number of input strings, even for binary alphabets. The complexity under a particular weighted edit distance remains open and seems non-trivial, since if Σ = {0, 1} and if the scores of insertions/deletions of 0 and of 1 are not equal then our reduction does not seem to hold.. Although CENTER STRING and MEDIAN STRING are NP-complete, there exist approximation algorithms with bounded errors [8] and heuristic algorithms that are used in practice [10, 19] . For example, given a finite language W over Σ , a set center (resp. set median) of W can be found in polynomial time and is an approximate center (resp. median) of W with performance ratio 2 (resp. 2 − 2 #W ). Note that we call set center (resp. set median) of W any string that minimizes the maximum (resp. the sum) of the distances to strings in the set W and belongs to W . An open question subsists: do these problems admit Polynomial Time Approximation Schemes?

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Non-negative matrix factorization and its application in blind sparse source separation with less sensors than sources Non-Negative Matrix Factorization (NMF) implies that a given nonnegative matrix is represented by a product of two non-negative matrices. In this paper, a factorization condition (consistent condition) on basis matrix is proposed firstly. For a given consistent basis matrix, although there exist infinite solutions (factorizations) generally, the sparse solution is unique with probability one, which can be obtained by solving linear programming problems. Although it is very difficult to find out the best basis matrix, an algorithm is developed for finding a suboptimal basis matrix. Finally, an application of NMF is proposed for blind sparse source separation with less sensors than sources. Many learning theory problems can be expressed in terms of matrix factorization. Recently, it has been found that non-negative matrix factorization [1] has several promising and exciting applications such as image coding, data mining, compression, information retrieval, etc.. Sparse representation of signals has been receiving a great deal of interest in recent years which also can be modelled by matrix factorization. In [2] was discussed sparse representation of signals by using large scale linear programming under given over-complete basis 1 (e.g., wavelets). The objective function linear programming is only based on sparsity of coefficients, however, the basis vectors are given in advance without localized features. Several improved FOCUSS-based algorithms (e.g., [4] ) were designed to solve under-determined linear inverse problem when both the dictionary and the sources are unknown. To avoid degenerate solution, the dictionary is assumed to be in a compact submanifold of R m×n (e.g., unit Frobenius-norm dictionary). In [1] , a non-negative matrix factorization approach was proposed to learn the parts of objects. From the results in [1] , we can see an essential benefit of NMF, that is, these basis images can be localized features of the original images. In the implementation algorithm, each basis is also normalized to eliminate a degeneracy.. This paper considers the following NMF model. where the X ∈ R n×K (K > 1) is a known data matrix, B = [b 1 · · · b m ] is a n × m basis matrix, S = [s ij ] m×K is a coefficient matrix. m > n, which implies that the basis is over-complete. X, B and S are non-negative matrices.. It is well known that there exist many solutions of the factorization (1) generally. However, it is not that for any given non-negative basis matrix B, there exists a non-negative coefficient matrix S such that (1) holds. For a basis matrix, if there is at least a non-negative matrix factorization as (1), then the basis matrix is said to be a consistent basis matrix. In this paper, a consistent basis matrix condition is proposed firstly. For given consistent basis matrix, the number of solution of (1) is then discussed. Under the sparsity measure of l 1 norm, the uniqueness result of sparse solution is obtained. Theoretically, among all the consistent basis matrices, there is the best basis, such that the corresponding coefficient matrix is the most sparse. Although it is remaining an open problem to find the best basis, we find that the basis of which the column vectors are composed by cluster centers of X is a good basis. In the next, the cluster center basis is obtained by using K-Means algorithm. At last, a application of NMF is discussed for blind sparse source separation with less sensors than sources.. Recently, under-determined blind source separation based on sparse representation has received much attention, e.g. [7, 8, 9, 10] , . In several references, the mixing matrix and sources are estimated by using maximum posterior approach [7, 8] or maximum likelihood approach [6] . However, this kinds of approaches are limited by poor convergence. Another approach is two steps approach, that is, the mixing matrix and the sources are estimated separately [5] . In [5] , the blind source separation is performed in frequency domain. A clustering algorithm is presented for estimation the mixing matrix in two-sensor case, and the sources are then estimated by minimizing 1-norm (shortest path separation criterion). In this paper, the clustering algorithm and minimum l 1 norm criterion are used for estimating the mixing matrix and sources, respectively. However, the approach in this paper originate the sparsity criterion of data representation. Under the non-negative conditions, the minimum l 1 norm solution is proved to be unique with probability one for more than two sensors case. The recoverability of sources based on minimum l 1 norm criterion is analyzed. A simulation example also shows that the sources can be recovered even if they are overlapped to some degree, and that more sensors replies more credit for recovering sources.. In this paper, a consistent basis matrix condition is proposed firstly. For given consistent basis matrix, the number of solution of (1) is then discussed. Under the sparsity measure of l 1 norm, the uniqueness result of sparse solution is obtained. Theoretically, among all the consistent basis matrices, there is the best basis, such that the corresponding coefficient matrix is the most sparse. Although it is remaining an open problem to search the best basis, we find that the basis matrix of which the column vectors are cluster centers of X is a suboptimal basis matrix. Finally, an application of NMF algorithm in this paper is discussed for blind sparse source separation with less sensors than sources. Nonnegative matrix factorization is discussed in this paper. A factorization condition on basis matrix is first proposed. For a given consistent basis matrix, although there exist infinite number of solutions (factorizations) generally, the sparse solution is unique with probability one, which can be obtained by using linear programming algorithm. This paper also presents an algorithm for finding a suboptimal basis matrix. This basis matrix is composed by data cluster centers which can guarantee that the coefficient matrix is very sparse. At last, an application of NMF is proposed for blind sparse source separation with less sensors than sources. Two simulation examples reveal the validity and performance of the algorithm in this paper. Using the approach in this paper, the sparse sources can be recovered even if the sources are overlapped to some degree. The fifteen outputs of which the first ten are recovered sources in Example 2 (it has been assumed that the number of sources is also unknown).

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