OpenRaiser/Intern-Atlas huggingface dataset:
A Framework for Providing E-Services to the Rural Areas using Wireless Ad Hoc and Sensor Networks
Venue: arXiv cs.OH 2007
Year: 2007

In recent years, the proliferation of mobile computing devices has driven a revolutionary change in the computing world. The nature of ubiquitous devices makes wireless networks the easiest solution for their interconnection. This has led to the rapid growth of several wireless systems like wireless ad hoc networks, wireless sensor networks etc. In this paper we have proposed a framework for rural development by providing various e-services to the rural areas with the help of wireless ad hoc and sensor networks. We have discussed how timely and accurate information could be collected from the rural areas using wireless technologies. In addition to this, we have also mentioned the technical and operational challenges that could hinder the implementation of such a framework in the rural areas in the developing countries.
An Efficient PKC-Based Security Architecture for Wireless Sensor Networks
Venue: arXiv cs.CR 2007
Year: 2007

In spite of previous widely held belief of the incompatibility of public key cryptography (PKC) schemes for wireless sensor networks (WSNs), some recent works have shown that, PKC based schemes could be implemented for such networks in some ways. The major challenge of employing a PKC scheme in wireless sensor network is posed by the limitations of resources of the tiny sensors. Considering this feature of the sensors, in this paper, we propose an efficient PKC based security architecture with relatively less resource requirements than those of the other previously proposed PKC schemes for WSN. Our security architecture comprises basically of two parts; a key handshaking scheme based on simple linear operations and the derivation of decryption key by a receiver node. Our architecture allows both base-station-to-node or node-to-base-station secure communications, and node-to-node secure communications. Analysis and simulation results show that, our proposed architecture ensures a good level of security for communications in the network and could effectively be implemented using the limited computation, memory and energy budgets of the current generation sensor nodes.
Interval Edge Colorings of Mobius Ladders
Venue: arXiv cs.DM 2007
Year: 2007

An interval edge t-coloring of a graph G is a proper edge coloring of G with colors 1,2...,t such that at least one edge of G is colored by color i,i=1,2...,t, and the edges incident with each vertex x are colored by d_{G}(x) consecutive colors, where d_{G}(x) is the degree of the vertex x in G. For Mobius ladders the existence of this coloring is proved and all possible numbers of colors in such colorings are found.
Reinforcement Learning with Linear Function Approximation and LQ control Converges
Venue: arXiv cs.LG 2007
Year: 2007

Reinforcement learning is commonly used with function approximation. However, very few positive results are known about the convergence of function approximation based RL control algorithms. In this paper we show that TD(0) and Sarsa(0) with linear function approximation is convergent for a simple class of problems, where the system is linear and the costs are quadratic (the LQ control problem). Furthermore, we show that for systems with Gaussian noise and non-completely observable states (the LQG problem), the mentioned RL algorithms are still convergent, if they are combined with Kalman filtering.
Testing Bipartiteness of Geometric Intersection Graphs
Venue: arXiv cs.CG 2007
Year: 2007

We show how to test the bipartiteness of an intersection graph of n line segments or simple polygons in the plane, or of balls in R^d, in time O(n log n). More generally we find subquadratic algorithms for connectivity and bipartiteness testing of intersection graphs of a broad class of geometric objects. For unit balls in R^d, connectivity testing has equivalent randomized complexity to construction of Euclidean minimum spanning trees, and hence is unlikely to be solved as efficiently as bipartiteness testing. For line segments or planar disks, testing k-colorability of intersection graphs for k>2 is NP-complete.
Fast generators for the Diffie-Hellman key agreement protocol and malicious standards
Venue: arXiv cs.CR 2007
Year: 2007

The Diffie-Hellman key agreement protocol is based on taking large powers of a generator of a prime-order cyclic group. Some generators allow faster exponentiation. We show that to a large extent, using the fast generators is as secure as using a randomly chosen generator. On the other hand, we show that if there is some case in which fast generators are less secure, then this could be used by a malicious authority to generate a standard for the Diffie-Hellman key agreement protocol which has a hidden trapdoor.
Quickest detection of a minimum of disorder times
Venue: arXiv cs.CE 2007
Year: 2007

A multi-source quickest detection problem is considered. Assume there are two independent Poisson processes $X^{1}$ and $X^{2}$ with disorder times $θ_{1}$ and $θ_{2}$, respectively; that is, the intensities of $X^1$ and $X^2$ change at random unobservable times $θ_1$ and $θ_2$, respectively. $θ_1$ and $θ_2$ are independent of each other and are exponentially distributed. Define $θ\triangleq θ_1 \wedge θ_2=\min\{θ_{1},θ_{2}\}$ . For any stopping time $τ$ that is measurable with respect to the filtration generated by the observations define a penalty function of the form \[ R_τ=\mathbb{P}(τ<θ)+c \mathbb{E}[(τ-θ)^{+}], \] where $c>0$ and $(τ-θ)^{+}$ is the positive part of $τ-θ$. It is of interest to find a stopping time $τ$ that minimizes the above performance index. Since both observations $X^{1}$ and $X^{2}$ reveal information about the disorder time $θ$, even this simple problem is more involved than solving the disorder problems for $X^{1}$ and $X^{2}$ separately. This problem is formulated in terms of a three dimensional sufficient statistic, and the corresponding optimal stopping problem is examined. A two dimensional optimal stopping problem whose optimal stopping time turns out to coincide with the optimal stopping time of the original problem for some range of parameters is also solved. The value function of this problem serves as a tight upper bound for the original problem's value function. The two solutions are characterized by iterating suitable functional operators.
Learning Unions of $ω(1)$-Dimensional Rectangles
Venue: arXiv cs.LG 2007
Year: 2007

We consider the problem of learning unions of rectangles over the domain $[b]^n$, in the uniform distribution membership query learning setting, where both b and n are "large". We obtain poly$(n, \log b)$-time algorithms for the following classes: - poly$(n \log b)$-way Majority of $O(\frac{\log(n \log b)} {\log \log(n \log b)})$-dimensional rectangles. - Union of poly$(\log(n \log b))$ many $O(\frac{\log^2 (n \log b)} {(\log \log(n \log b) \log \log \log (n \log b))^2})$-dimensional rectangles. - poly$(n \log b)$-way Majority of poly$(n \log b)$-Or of disjoint $O(\frac{\log(n \log b)} {\log \log(n \log b)})$-dimensional rectangles. Our main algorithmic tool is an extension of Jackson's boosting- and Fourier-based Harmonic Sieve algorithm [Jackson 1997] to the domain $[b]^n$, building on work of [Akavia, Goldwasser, Safra 2003]. Other ingredients used to obtain the results stated above are techniques from exact learning [Beimel, Kushilevitz 1998] and ideas from recent work on learning augmented $AC^{0}$ circuits [Jackson, Klivans, Servedio 2002] and on representing Boolean functions as thresholds of parities [Klivans, Servedio 2001].
Joint fixed-rate universal lossy coding and identification of continuous-alphabet memoryless sources
Venue: arXiv cs.IT 2007
Year: 2007

The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any compactly parametrized family of $\R^d$-valued i.i.d. sources with absolutely continuous distributions satisfying appropriate smoothness and Vapnik--Chervonenkis learnability conditions, admits a joint scheme for universal lossy block coding and parameter estimation, such that when the block length $n$ tends to infinity, the overhead per-letter rate and the distortion redundancies converge to zero as $O(n^{-1}\log n)$ and $O(\sqrt{n^{-1}\log n})$, respectively. Moreover, the active source can be determined at the decoder up to a ball of radius $O(\sqrt{n^{-1} \log n})$ in variational distance, asymptotically almost surely. The system has finite memory length equal to the block length, and can be thought of as blockwise application of a time-invariant nonlinear filter with initial conditions determined from the previous block. Comparisons are presented with several existing schemes for universal vector quantization, which do not include parameter estimation explicitly, and an extension to unbounded distortion measures is outlined. Finally, finite mixture classes and exponential families are given as explicit examples of parametric sources admitting joint universal compression and modeling schemes of the kind studied here.
Unary Primitive Recursive Functions
Venue: arXiv cs.SC 2007
Year: 2007

In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets.
Protocols for Kak's Cubic Cipher and Diffie-Hellman Based Asymmetric Oblivious Key Exchange
Venue: arXiv cs.CR 2007
Year: 2007

This paper presents protocols for Kak's cubic transformation and proposes a modification to Diffie-Hellman key exchange protocol in order to achieve asymmetric oblivious exchange of keys.
Geometric representation of graphs in low dimension
Venue: arXiv cs.DM 2007
Year: 2007

We give an efficient randomized algorithm to construct a box representation of any graph G on n vertices in $1.5 (Δ+ 2) \ln n$ dimensions, where $Δ$ is the maximum degree of G. We also show that $\boxi(G) \le (Δ+ 2) \ln n$ for any graph G. Our bound is tight up to a factor of $\ln n$. We also show that our randomized algorithm can be derandomized to get a polynomial time deterministic algorithm. Though our general upper bound is in terms of maximum degree $Δ$, we show that for almost all graphs on n vertices, its boxicity is upper bound by $c\cdot(d_{av} + 1) \ln n$ where d_{av} is the average degree and c is a small constant. Also, we show that for any graph G, $\boxi(G) \le \sqrt{8 n d_{av} \ln n}$, which is tight up to a factor of $b \sqrt{\ln n}$ for a constant b.
Tromino tilings of Domino-Deficient Rectangles
Venue: arXiv cs.DM 2007
Year: 2007

We consider tromino tilings of $m\times n$ domino-deficient rectangles, where $3|(mn-2)$ and $m,n\geq0$, and characterize all cases of domino removal that admit such tilings, thereby settling the open problem posed by J. M. Ash and S. Golomb in \cite {marshall}. Based on this characterization, we design a procedure for constructing such a tiling if one exists. We also consider the problem of counting such tilings and derive the exact formula for the number of tilings for $2\times(3t+1)$ rectangles, the exact generating function for $4\times(3t+2)$ rectangles, where $t\geq0$, and an upper bound on the number of tromino tilings for $m\times n$ domino-deficient rectangles. We also consider general 2-deficiency in $n\times4$ rectangles, where $n\geq8$, and characterize all pairs of squares which do not permit a tromino tiling.
The Minimal Cost Algorithm for Off-Line Diagnosability of Discrete Event Systems
Venue: arXiv cs.AI 2007
Year: 2007

The failure diagnosis for {\it discrete event systems} (DESs) has been given considerable attention in recent years. Both on-line and off-line diagnostics in the framework of DESs was first considered by Lin Feng in 1994, and particularly an algorithm for diagnosability of DESs was presented. Motivated by some existing problems to be overcome in previous work, in this paper, we investigate the minimal cost algorithm for diagnosability of DESs. More specifically: (i) we give a generic method for judging a system's off-line diagnosability, and the complexity of this algorithm is polynomial-time; (ii) and in particular, we present an algorithm of how to search for the minimal set in all observable event sets, whereas the previous algorithm may find {\it non-minimal} one.
Equality of complexity classes P and NP: Linear programming formulation of the quadratic assignment problem
Venue: arXiv cs.CC 2007
Year: 2007

In this paper, we present a polynomial-sized linear programming formulation of the Quadratic Assignment Problem (QAP). The proposed linear program is a network flow-based model. Hence, it provides for the solution of the QAP in polynomial time. Computational testing and results are discussed.
The Connectivity of Boolean Satisfiability: Computational and Structural Dichotomies
Venue: arXiv cs.CC 2007
Year: 2007

Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and connectivity of the solution space. Motivated by this work, we study structural and connectivity-related properties of the space of solutions of Boolean satisfiability problems and establish various dichotomies in Schaefer's framework. On the structural side, we obtain dichotomies for the kinds of subgraphs of the hypercube that can be induced by the solutions of Boolean formulas, as well as for the diameter of the connected components of the solution space. On the computational side, we establish dichotomy theorems for the complexity of the connectivity and st-connectivity questions for the graph of solutions of Boolean formulas. Our results assert that the intractable side of the computational dichotomies is PSPACE-complete, while the tractable side - which includes but is not limited to all problems with polynomial time algorithms for satisfiability - is in P for the st-connectivity question, and in coNP for the connectivity question. The diameter of components can be exponential for the PSPACE-complete cases, whereas in all other cases it is linear; thus, small diameter and tractability of the connectivity problems are remarkably aligned. The crux of our results is an expressibility theorem showing that in the tractable cases, the subgraphs induced by the solution space possess certain good structural properties, whereas in the intractable cases, the subgraphs can be arbitrary.
Improved Approximate String Matching and Regular Expression Matching on Ziv-Lempel Compressed Texts
Venue: arXiv cs.DS 2007
Year: 2007

We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck.
Measuring Fundamental Properties of Real-World Complex Networks
Venue: arXiv cs.NI 2007
Year: 2007

Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these procedures eventually lead to samples large enough to be representative of the whole, at least concerning some key properties. This has crucial impact on network modeling and simulation, which rely on these properties. Recent contributions proved that this approach may be misleading, but no solution has been proposed. We provide here the first practical way to distinguish between cases where it is indeed misleading, and cases where the observed properties may be trusted. It consists in studying how the properties of interest evolve when the sample grows, and in particular whether they reach a steady state or not. In order to illustrate this method and to demonstrate its relevance, we apply it to data-sets on complex network measurements that are representative of the ones commonly used. The obtained results show that the method fulfills its goals very well. We moreover identify some properties which seem easier to evaluate in practice, thus opening interesting perspectives.
VPSPACE and a Transfer Theorem over the Reals
Venue: arXiv cs.CC 2007
Year: 2007

We introduce a new class VPSPACE of families of polynomials. Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space. Our main theorem is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently then the class PAR of decision problems that can be solved in parallel polynomial time over the real numbers collapses to P. As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate over the reals P from NP, or even from PAR.
On Shift Sequences for Interleaved Construction of Sequence Sets with Low Correlation
Venue: arXiv cs.IT 2007
Year: 2007

Construction of signal sets with low correlation property is of interest to designers of CDMA systems. One of the preferred ways of constructing such sets is the interleaved construction which uses two sequences a and b with 2-level autocorrelation and a shift sequence e. The shift sequence has to satisfy certain conditions for the resulting signal set to have low correlation properties. This article shows that the conditions reported in literature are too strong and gives a version which results in more number of shift sequences. An open problem on the existence of shift sequences for attaining an interleaved set with maximum correlation value bounded by v+2 is also taken up and solved.
Bounds on the coefficients of the characteristic and minimal polynomials
Venue: arXiv cs.SC 2007
Year: 2007

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise input-dependant bounds on these coefficients. Such bounds are e.g. useful to perform deterministic chinese remaindering of the characteristic or minimal polynomial of an integer matrix.
The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link, Part II: vector systems
Venue: arXiv cs.IT 2007
Year: 2007

In part I, we reviewed how Shannon's classical notion of capacity is not sufficient to characterize a noisy communication channel if the channel is intended to be used as part of a feedback loop to stabilize an unstable scalar linear system. While classical capacity is not enough, a sense of capacity (parametrized by reliability) called "anytime capacity" is both necessary and sufficient for channel evaluation in this context. The rate required is the log of the open-loop system gain and the required reliability comes from the desired sense of stability. Sufficiency is maintained even in cases with noisy observations and without any explicit feedback between the observer and the controller. This established the asymptotic equivalence between scalar stabilization problems and delay-universal communication problems with feedback. Here in part II, the vector-state generalizations are established and it is the magnitudes of the unstable eigenvalues that play an essential role. To deal with such systems, the concept of the anytime rate-region is introduced. This is the region of rates that the channel can support while still meeting potentially different anytime reliability targets for parallel message streams. All the scalar results generalize on an eigenvalue by eigenvalue basis. When there is no explicit feedback of the noisy channel outputs, the intrinsic delay of the unstable system tells us what the feedback delay needs to be while evaluating the anytime-rate-region for the channel. An example involving a binary erasure channel is used to illustrate how differentiated service is required in any separation-based control architecture.
Canonical decomposition of catenation of factorial languages
Venue: arXiv cs.LO 2007
Year: 2007

According to a previous result by S. V. Avgustinovich and the author, each factorial language admits a unique canonical decomposition to a catenation of factorial languages. In this paper, we analyze the appearance of the canonical decomposition of a catenation of two factorial languages whose canonical decompositions are given.
Nonextensive Pythagoras' Theorem
Venue: arXiv cs.IT 2007
Year: 2007

Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theorem in the generalized nonextensive formalism is established in (Dukkipati at el., Physica A, 361 (2006) 124-138). In this paper we give a detailed account of it.
On Conditional Branches in Optimal Decision Trees
Venue: arXiv cs.PF 2007
Year: 2007

The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests in order to determine one of $n$ outcome events. The process of finding an optimal alphabetic binary tree for a known probability distribution on outcome events usually has the underlying assumption that the cost (time) per decision is uniform and thus independent of the outcome of the decision. This assumption, however, is incorrect in the case of software to be optimized for a given microprocessor, e.g., in compiling switch statements or in fine-tuning program bottlenecks. The operation of the microprocessor generally means that the cost for the more likely decision outcome can or will be less -- often far less -- than the less likely decision outcome. Here we formulate a variety of $O(n^3)$-time $O(n^2)$-space dynamic programming algorithms to solve such optimal binary decision tree problems, optimizing for the behavior of processors with predictive branch capabilities, both static and dynamic. In the static case, we use existing results to arrive at entropy-based performance bounds. Solutions to this formulation are often faster in practice than ``optimal'' decision trees as formulated in the literature, and, for small problems, are easily worth the extra complexity in finding the better solution. This can be applied in fast implementation of decoding Huffman codes.
On numerical stability of recursive present value computation method
Venue: arXiv cs.CE 2007
Year: 2007

We analyze numerical stability of a recursive computation scheme of present value (PV) amd show that the absolute error increases exponentially for positive discount rates. We show that reversing the direction of calculations in the recurrence equation yields a robust PV computation routine.