OpenRaiser/Intern-Atlas huggingface dataset:
Estimation of Small s-t Reliabilities in Acyclic Networks
Venue: arXiv cs.DM 2007
Year: 2007

In the classical s-t network reliability problem a fixed network G is given including two designated vertices s and t (called terminals). The edges are subject to independent random failure, and the task is to compute the probability that s and t are connected in the resulting network, which is known to be #P-complete. In this paper we are interested in approximating the s-t reliability in case of a directed acyclic original network G. We introduce and analyze a specialized version of the Monte-Carlo algorithm given by Karp and Luby. For the case of uniform edge failure probabilities, we give a worst-case bound on the number of samples that have to be drawn to obtain an epsilon-delta approximation, being sharper than the original upper bound. We also derive a variance reduction of the estimator which reduces the expected number of iterations to perform to achieve the desired accuracy when applied in conjunction with different stopping rules. Initial computational results on two types of random networks (directed acyclic Delaunay graphs and a slightly modified version of a classical random graph) with up to one million vertices are presented. These results show the advantage of the introduced Monte-Carlo approach compared to direct simulation when small reliabilities have to be estimated and demonstrate its applicability on large-scale instances.
A Knowledge-Based Analysis of Global Function Computation
Venue: arXiv cs.DC 2007
Year: 2007

Consider a distributed system N in which each agent has an input value and each communication link has a weight. Given a global function, that is, a function f whose value depends on the whole network, the goal is for every agent to eventually compute the value f(N). We call this problem global function computation. Various solutions for instances of this problem, such as Boolean function computation, leader election, (minimum) spanning tree construction, and network determination, have been proposed, each under particular assumptions about what processors know about the system and how this knowledge can be acquired. We give a necessary and sufficient condition for the problem to be solvable that generalizes a number of well-known results. We then provide a knowledge-based (kb) program (like those of Fagin, Halpern, Moses, and Vardi) that solves global function computation whenever possible. Finally, we improve the message overhead inherent in our initial kb program by giving a counterfactual belief-based program that also solves the global function computation whenever possible, but where agents send messages only when they believe it is necessary to do so. The latter program is shown to be implemented by a number of well-known algorithms for solving leader election.
An exploratory study of Google Scholar
Venue: arXiv cs.DL 2007
Year: 2007

The paper discusses and analyzes the scientific search service Google Scholar (GS). The focus is on an exploratory study which investigates the coverage of scientific serials in GS. The study shows deficiencies in the coverage and up-to-dateness of the GS index. Furthermore, the study points up which Web servers are the most important data providers for this search service and which information sources are highly represented. We can show that there is a relatively large gap in Google Scholars coverage of German literature as well as weaknesses in the accessibility of Open Access content. Keywords: Search engines, Digital libraries, Worldwide Web, Serials, Electronic journals
GCP: Gossip-based Code Propagation for Large-scale Mobile Wireless Sensor Networks
Venue: arXiv cs.NI 2007
Year: 2007

Wireless sensor networks (WSN) have recently received an increasing interest. They are now expected to be deployed for long periods of time, thus requiring software updates. Updating the software code automatically on a huge number of sensors is a tremendous task, as ''by hand'' updates can obviously not be considered, especially when all participating sensors are embedded on mobile entities. In this paper, we investigate an approach to automatically update software in mobile sensor-based application when no localization mechanism is available. We leverage the peer-to-peer cooperation paradigm to achieve a good trade-off between reliability and scalability of code propagation. More specifically, we present the design and evaluation of GCP ({\emph Gossip-based Code Propagation}), a distributed software update algorithm for mobile wireless sensor networks. GCP relies on two different mechanisms (piggy-backing and forwarding control) to improve significantly the load balance without sacrificing on the propagation speed. We compare GCP against traditional dissemination approaches. Simulation results based on both synthetic and realistic workloads show that GCP achieves a good convergence speed while balancing the load evenly between sensors.
Interactive Small-Step Algorithms II: Abstract State Machines and the<br> Characterization Theorem
Venue: arXiv cs.LO 2007
Year: 2007

In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step algorithms. This was accomplished on the basis of axiomatizations of these classes of algorithms. In Part I (Interactive Small-Step Algorithms I: Axiomatization), the axiomatization was extended to cover interactive small-step algorithms that are not necessarily ordinary. This means that the algorithms (1) can complete a step without necessarily waiting for replies to all queries from that step and (2) can use not only the environment's replies but also the order in which the replies were received. In order to prove the thesis for algorithms of this generality, we extend here the definition of abstract state machines to incorporate explicit attention to the relative timing of replies and to the possible absence of replies. We prove the characterization theorem for extended abstract state machines with respect to general algorithms as axiomatized in Part I.
How to be correct, lazy and efficient ?
Venue: arXiv cs.PL 2007
Year: 2007

This paper is an introduction to Lambdix, a lazy Lisp interpreter implemented at the Research Laboratory of Paris XI University (Laboratoire de Recherche en Informatique, Orsay). Lambdix was devised in the course of an investigation into the relationship between the semantics of programming languages and their implementation; it was used to demonstrate that in the Lisp domain, semantic correctness is consistent with efficiency, contrary to what has often been claimed. The first part of the paper is an overview of well-known semantic difficulties encountered by Lisp as well as an informal presentation of Lambdix; it is shown that the difficulties which Lisp encouters do not arise in Lambdix. The second part is about efficiency in implementation models. It explains why Lambdix is better suited for lazy evaluation than previous models. The section ends by giving comparative execution time tables.
Plotkin construction: rank and kernel
Venue: arXiv cs.IT 2007
Year: 2007

Given two binary codes of length n, using Plotkin construction we obtain a code of length 2n. The construction works for linear and nonlinear codes. For the linear case, it is straightforward to see that the dimension of the final code is the sum of the dimensions of the starting codes. For nonlinear codes, the rank and the dimension of the kernel are standard mesures of linearity. In this report, we prove that both parameters are also the sum of the corresponding ones of the starting codes.
Chain of Separable Binary Goppa Codes and their Minimal Distance
Venue: arXiv cs.IT 2007
Year: 2007

It is shown that subclasses of separable binary Goppa codes, $Γ(L,G)$ - codes, with $L=\{α\in GF(2^{2l}):G(α)\neq 0 \}$ and special Goppa polynomials G(x) can be presented as a chain of embedded codes. The true minimal distance has been obtained for all codes of the chain.
Complementary algorithms for graphs and percolation
Venue: arXiv cs.DS 2007
Year: 2007

A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph representation and so, in concert, can arbitrarily modify any graph. Since the clusters of a percolation model may be described as simple connected graphs, an efficient Monte Carlo scheme can be constructed that uses the algorithms to sweep the occupation probability back and forth between two turning points. This approach concentrates computational sampling time within a region of interest. A high precision value of pc = 0.59274603(9) was thus obtained, by Mersenne twister, for the two dimensional square site percolation threshold.
Cooperative Beamforming for Wireless Ad Hoc Networks
Venue: arXiv cs.IT 2007
Year: 2007

Via collaborative beamforming, nodes in a wireless network are able to transmit a common message over long distances in an energy efficient fashion. However, the process of making available the same message to all collaborating nodes introduces delays. In this paper, a MAC-PHY cross-layer scheme is proposed that enables collaborative beamforming at significantly reduced collaboration overhead. It consists of two phases. In the first phase, nodes transmit locally in a random access time-slotted fashion. Simultaneous transmissions from multiple source nodes are viewed as linear mixtures of all transmitted packets. In the second phase, a set of collaborating nodes, acting as a distributed antenna system, beamform the received analog waveform to one or more faraway destinations. This step requires multiplication of the received analog waveform by a complex weight, which is independently computed by each cooperating node, and which allows packets bound to the same destination to add coherently at the destination node. Assuming that each node has access to location information, the proposed scheme can achieve high throughput, which in certain cases exceeds one. An analysis of the symbol error probability corresponding to the proposed scheme is provided.
Cooperative game theory and the Gaussian interference channel
Venue: arXiv cs.IT 2007
Year: 2007

In this paper we discuss the use of cooperative game theory for analyzing interference channels. We extend our previous work, to games with N players as well as frequency selective channels and joint TDM/FDM strategies. We show that the Nash bargaining solution can be computed using convex optimization techniques. We also show that the same results are applicable to interference channels where only statistical knowledge of the channel is available. Moreover, for the special case of two players $2\times K$ frequency selective channel (with K frequency bins) we provide an $O(K \log_2 K)$ complexity algorithm for computing the Nash bargaining solution under mask constraint and using joint FDM/TDM strategies. Simulation results are also provided.
Relations between random coding exponents and the statistical physics of random codes
Venue: arXiv cs.IT 2007
Year: 2007

The partition function pertaining to finite--temperature decoding of a (typical) randomly chosen code is known to have three types of behavior, corresponding to three phases in the plane of rate vs. temperature: the {\it ferromagnetic phase}, corresponding to correct decoding, the {\it paramagnetic phase}, of complete disorder, which is dominated by exponentially many incorrect codewords, and the {\it glassy phase} (or the condensed phase), where the system is frozen at minimum energy and dominated by subexponentially many incorrect codewords. We show that the statistical physics associated with the two latter phases are intimately related to random coding exponents. In particular, the exponent associated with the probability of correct decoding at rates above capacity is directly related to the free energy in the glassy phase, and the exponent associated with probability of error (the error exponent) at rates below capacity, is strongly related to the free energy in the paramagnetic phase. In fact, we derive alternative expressions of these exponents in terms of the corresponding free energies, and make an attempt to obtain some insights from these expressions. Finally, as a side result, we also compare the phase diagram associated with a simple finite-temperature universal decoder for discrete memoryless channels, to that of the finite--temperature decoder that is aware of the channel statistics.
On the Self-stabilization of Mobile Robots in Graphs
Venue: arXiv cs.DS 2007
Year: 2007

Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The contribution of this paper is threefold. First, we present a new model for studying mobile entities in networks subject to transient faults. Our model differs from the classical robot model because robots have constraints about the paths they are allowed to follow, and from the classical agent model because the number of agents remains fixed throughout the execution of the protocol. Second, in this model, we study the possibility of designing self-stabilizing algorithms when those algorithms are run by mobile robots (or agents) evolving on a graph. We concentrate on the core building blocks of robot and agents problems: naming and leader election. Not surprisingly, when no constraints are given on the network graph topology and local execution model, both problems are impossible to solve. Finally, using minimal hypothesis with respect to impossibility results, we provide deterministic and probabilistic solutions to both problems, and show equivalence of these problems by an algorithmic reduction mechanism.
Homogeneous temporal activity patterns in a large online communication space
Venue: arXiv cs.NI 2007
Year: 2007

The many-to-many social communication activity on the popular technology-news website Slashdot has been studied. We have concentrated on the dynamics of message production without considering semantic relations and have found regular temporal patterns in the reaction time of the community to a news-post as well as in single user behavior. The statistics of these activities follow log-normal distributions. Daily and weekly oscillatory cycles, which cause slight variations of this simple behavior, are identified. A superposition of two log-normal distributions can account for these variations. The findings are remarkable since the distribution of the number of comments per users, which is also analyzed, indicates a great amount of heterogeneity in the community. The reader may find surprising that only a few parameters allow a detailed description, or even prediction, of social many-to-many information exchange in this kind of popular public spaces.
Opportunism in Multiuser Relay Channels: Scheduling, Routing and Spectrum Reuse
Venue: arXiv cs.IT 2007
Year: 2007

In order to understand the key merits of multiuser diversity techniques in relay-assisted cellular multihop networks, this paper analyzes the spectral efficiency of opportunistic (i.e., channel-aware) scheduling algorithms over a fading multiuser relay channel with $K$ users in the asymptotic regime of large (but finite) number of users. Using tools from extreme-value theory, we characterize the limiting distribution of spectral efficiency focusing on Type I convergence and utilize it in investigating the large system behavior of the multiuser relay channel as a function of the number of users and physical channel signal-to-noise ratios (SNRs). Our analysis results in very accurate formulas in the large (but finite) $K$ regime, provides insights on the potential performance enhancements from multihop routing and spectrum reuse policies in the presence of multiuser diversity gains from opportunistic scheduling and helps to identify the regimes and conditions in which relay-assisted multiuser communication provides a clear advantage over direct multiuser communication.
On Compact Routing for the Internet
Venue: arXiv cs.NI 2007
Year: 2007

While there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer routing tables of sizes that scale logarithmically with the network size, we demonstrate in this paper that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic routing table size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale ``indefinitely.''
On Semimeasures Predicting Martin-Loef Random Sequences
Venue: arXiv cs.IT 2007
Year: 2007

Solomonoff's central result on induction is that the posterior of a universal semimeasure M converges rapidly and with probability 1 to the true sequence generating posterior mu, if the latter is computable. Hence, M is eligible as a universal sequence predictor in case of unknown mu. Despite some nearby results and proofs in the literature, the stronger result of convergence for all (Martin-Loef) random sequences remained open. Such a convergence result would be particularly interesting and natural, since randomness can be defined in terms of M itself. We show that there are universal semimeasures M which do not converge for all random sequences, i.e. we give a partial negative answer to the open problem. We also provide a positive answer for some non-universal semimeasures. We define the incomputable measure D as a mixture over all computable measures and the enumerable semimeasure W as a mixture over all enumerable nearly-measures. We show that W converges to D and D to mu on all random sequences. The Hellinger distance measuring closeness of two distributions plays a central role.
Space and camera path reconstruction for omni-directional vision
Venue: arXiv cs.CV 2007
Year: 2007

In this paper, we address the inverse problem of reconstructing a scene as well as the camera motion from the image sequence taken by an omni-directional camera. Our structure from motion results give sharp conditions under which the reconstruction is unique. For example, if there are three points in general position and three omni-directional cameras in general position, a unique reconstruction is possible up to a similarity. We then look at the reconstruction problem with m cameras and n points, where n and m can be large and the over-determined system is solved by least square methods. The reconstruction is robust and generalizes to the case of a dynamic environment where landmarks can move during the movie capture. Possible applications of the result are computer assisted scene reconstruction, 3D scanning, autonomous robot navigation, medical tomography and city reconstructions.
On the Complexity of the Minimum Cost Homomorphism Problem for Reflexive Multipartite Tournaments
Venue: arXiv cs.DM 2007
Year: 2007

For digraphs $D$ and $H$, a mapping $f: V(D)\dom V(H)$ is a homomorphism of $D$ to $H$ if $uv\in A(D)$ implies $f(u)f(v)\in A(H).$ For a fixed digraph $H$, the homomorphism problem is to decide whether an input digraph $D$ admits a homomorphism to $H$ or not, and is denoted as HOMP($H$). Digraphs are allowed to have loops, but not allowed to have parallel arcs. A natural optimization version of the homomorphism problem is defined as follows. If each vertex $u \in V(D)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of the homomorphism $f$ is $\sum_{u\in V(D)}c_{f(u)}(u)$. For each fixed digraph $H$, we have the {\em minimum cost homomorphism problem for} $H$ and denote it as MinHOMP($H$). The problem is to decide, for an input graph $D$ with costs $c_i(u),$ $u \in V(D), i\in V(H)$, whether there exists a homomorphism of $D$ to $H$ and, if one exists, to find one of minimum cost. In a recent paper, we posed a problem of characterizing polynomial time solvable and NP-hard cases of the minimum cost homomorphism problem for acyclic multipartite tournaments with possible loops (w.p.l.). In this paper, we solve the problem for reflexive multipartite tournaments and demonstrate a considerate difficulty of the problem for the whole class of multipartite tournaments w.p.l. using, as an example, acyclic 3-partite tournaments of order 4 w.p.l.\footnote{This paper was submitted to Discrete Mathematics on April 6, 2007}
Secrecy Capacity Region of Binary and Gaussian Multiple Access Channels
Venue: arXiv cs.IT 2007
Year: 2007

A generalized multiple access channel (GMAC) with one confidential message set is studied, where two users (users 1 and 2) attempt to transmit common information to a destination, and user 1 also has confidential information intended for the destination. Moreover, user 1 wishes to keep its confidential information as secret as possible from user 2. A deterministic GMAC is first studied, and the capacity-equivocation region and the secrecy capacity region are obtained. Two main classes of the GMAC are then studied: the binary GMAC and the Gaussian GMAC. For both channels, the capacity-equivocation region and the secrecy capacity region are established.
Fast Recursive Coding Based on Grouping of Symbols
Venue: arXiv cs.IT 2007
Year: 2007

A novel fast recursive coding technique is proposed. It operates with only integer values not longer 8 bits and is multiplication free. Recursion the algorithm is based on indirectly provides rather effective coding of symbols for very large alphabets. The code length for the proposed technique can be up to 20-30% less than for arithmetic coding and, in the worst case it is only by 1-3% larger.
Optimal strategies in the average consensus problem
Venue: arXiv cs.MA 2007
Year: 2007

We prove that for a set of communicating agents to compute the average of their initial positions (average consensus problem), the optimal topology of communication is given by a de Bruijn's graph. Consensus is then reached in a finitely many steps. A more general family of strategies, constructed by block Kronecker products, is investigated and compared to Cayley strategies.
Can Alice and Bob be random: a study on human playing zero knowledge protocols
Venue: arXiv cs.CR 2007
Year: 2007

The research described in this abstract was initiated by discussions between the author and Giovanni Di Crescenzo in Barcelona in early 2004. It was during Advanced Course on Contemporary Cryptology that Di Crescenzo gave a course on zero knowledge protocols (ZKP), see [1]. After that course we started to play with unorthodox ideas for breaking ZKP, especially one based on graph 3-coloring. It was chosen for investigation because it is being considered as a "benchmark" ZKP, see [2], [3]. At this point we briefly recall such a protocol's description.