Proceedings 2001 IEEE International Conference on Cluster Computing

8-11 Oct. 2001

Filter Results

Displaying Results 1 - 25 of 67
  • Improved inapproximability results for MaxClique, chromatic number and approximate graph coloring

    Publication Year: 2001, Page(s):600 - 609
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB) | HTML iconHTML

    The author presents improved inapproximability results for three problems: the problem of finding the maximum clique size in a graph, the problem of finding the chromatic number of a graph, and the problem of coloring a graph with a small chromatic number with a small number of colors. J. Hastad's (1996) result shows that the maximum clique size in a graph with n vertices is inapproximable in poly... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Distributions on level-sets with applications to approximation algorithms

    Publication Year: 2001, Page(s):588 - 597
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (272 KB) | HTML iconHTML

    We consider a family of distributions on fixed-weight vectors in {0, 1}t; these distributions enjoy certain negative correlation properties and also satisfy pre-specified conditions on their marginal distributions. We show the existence of such families, and present a linear-time algorithm to sample from them. This yields improved approximation algorithms for the following problems: (a)... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Randomly colouring graphs with lower bounds on girth and maximum degree

    Publication Year: 2001, Page(s):579 - 587
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (368 KB) | HTML iconHTML

    We consider the problem of generating a random q-colouring of a graph G=(V, E). We consider the simple Glauber Dynamics chain. We show that if the maximum degree Δ>cl ln n and the girth g>c2 ln ln n (n=|V|), then this chain mixes rapidly provided C1, C2 are sufficiently large, q/A>β, where β≈1.763 is the root of β=e1... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Designing networks incrementally

    Publication Year: 2001, Page(s):406 - 415
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (240 KB) | HTML iconHTML

    We consider the problem of incrementally designing a network to route demand to a single sink on an underlying metric space. We are given cables whose costs per unit length scale in a concave fashion with capacity. Under certain natural restrictions on the costs (called the Access Network Design constraints), we present a simple and efficient randomized algorithm that is competitive to the minimum... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A replacement for Voronoi diagrams of near linear size

    Publication Year: 2001, Page(s):94 - 103
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB) | HTML iconHTML

    For a set P of n points in Rd, we define a new type of space decomposition. The new diagram provides an ε-approximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d≥2. This contrasts with the standard Voronoi diagram that has Ω (n[d2]/) complexity in the worst case. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Lower bounds for matrix product

    Publication Year: 2001, Page(s):358 - 367
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB) | HTML iconHTML

    We prove lower bounds on the number of product gates in bilinear and quadratic circuits that compute the product of two n × n matrices over finite fields. In particular we obtain the following results: 1. We show that the number of product gates in any bilinear (or quadratic) circuit that computes the product of two n × n matrices over GF(2) is at least 3n2 o(n2).... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Glauber dynamics on trees and hyperbolic graphs

    Publication Year: 2001, Page(s):568 - 578
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (312 KB) | HTML iconHTML

    We study discrete time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We show that the relaxation time (defined as the reciprocal of the spectral gap 1-λ2) for the dynamics on trees and on certain hyperbolic graphs, is polynomial in n. For these hyperbolic gra... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Ramsey-type theorem for metric spaces and its applications for metrical task systems and related problems

    Publication Year: 2001, Page(s):396 - 405
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (296 KB) | HTML iconHTML

    The paper gives a nearly logarithmic lower bound on the randomized competitive ratio for a Metrical Task Systems model (A. Borodin et al., 1992). This implies a similar lower bound for the extensively studied K-server problem. Our proof is based on proving a Ramsey-type theorem for metric spaces. In particular, we prove that in every metric space there exists a large subspace which is approximatel... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Clustering motion

    Publication Year: 2001, Page(s):84 - 93
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (232 KB) | HTML iconHTML

    Given a set of moving points in Rd, we show that one can cluster them in advance, using a small number of clusters, so that at any point in time this static clustering is competitive with the optimal k-centre clustering of the point-set at this point in time. The advantage of this approach is that it avoids the usage of kinetic data structures and as such it does not need to update the ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Approximation algorithms for the job interval selection problem and related scheduling problems

    Publication Year: 2001, Page(s):348 - 356
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (256 KB) | HTML iconHTML

    The authors consider the job interval selection problem (JISP), a simple scheduling model with a rich history and numerous applications. Special cases of this problem include the so-called real-time scheduling problem (also known as the throughput maximization problem) in single and multiple machine environments. In these special cases we have to maximize the number of jobs scheduled between their... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the average-case hardness of CVP

    Publication Year: 2001, Page(s):308 - 317
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (232 KB) | HTML iconHTML

    We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. We assume that there is an efficient algorithm which can approximately solve a random instance of CVP, with a non-trivial success probability. For lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (i... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Arc-disjoint paths in expander digraphs

    Publication Year: 2001, Page(s):558 - 567
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (408 KB) | HTML iconHTML

    Given a digraph D=(V, A) and a set of κ pairs of vertices in V, we are interested in finding for each pair (xi, yi), a directed path connecting xi to yi, such that the set of κ paths so found is arc-disjoint. For arbitrary graphs, the problem is 𝒩𝒫-complete, even for κ=2. We present a polynomial time randomized algorithm for f... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Linear-time recognition of circular-arc graphs

    Publication Year: 2001, Page(s):386 - 394
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (224 KB) | HTML iconHTML

    A graph G is a circular-arc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if the corresponding arcs intersect. We give a linear time bound for recognizing this class of graphs. When G is a member of the class, the algorithm gives a certificate in the form of a set of arcs that realize it. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the complexity of many faces in arrangements of circles

    Publication Year: 2001, Page(s):74 - 83
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (216 KB) | HTML iconHTML

    We obtain improved bounds on the complexity of m distinct faces in an arrangement of n circles and in an arrangement of n unit circles. The bounds are worst-case tight for unit circles, and, for general circles, they nearly coincide with the best known bounds for the number of incidences between m points and n circles. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • An iterative rounding 2-approximation algorithm for the element connectivity problem

    Publication Year: 2001, Page(s):339 - 347
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (216 KB) | HTML iconHTML

    In the survivable network design problem (SNDP), given an undirected graph and values rij for each pair of vertices i and j, we attempt to find a minimum-cost subgraph such that there are rij disjoint paths between vertices i and j. In the edge connected version of this problem (EC-SNDP), these paths must be edge-disjoint. In the vertex connected version of the problem (VC-SN... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Algorithmic applications of low-distortion geometric embeddings

    Publication Year: 2001, Page(s):10 - 33
    Cited by:  Papers (27)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (504 KB) | HTML iconHTML

    The author surveys algorithmic results obtained using low-distortion embeddings of metric spaces into (mostly) normed spaces. He shows that low-distortion embeddings provide a powerful and versatile toolkit for solving algorithmic problems. Their fundamental nature makes them applicable in a variety of diverse settings, while their relation to rich mathematical fields (e.g., functional analysis) e... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The confluence of ground term rewrite systems is decidable in polynomial time

    Publication Year: 2001, Page(s):298 - 307
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (240 KB) | HTML iconHTML

    The confluence property of ground (i.e., variable-free) term rewrite systems (GTRS) is well-known to be decidable. This was proved independently by M. Dauchet et al. (1987; 1990) and by M. Oyamaguchi (1987) using tree automata techniques and ground tree transducer techniques (originated from this problem), yielding EXPTIME decision procedures (PSPACE for strings). Since then, it has been a well-kn... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Unique sink orientations of cubes

    Publication Year: 2001, Page(s):547 - 555
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (288 KB) | HTML iconHTML

    Suppose we are given (the edge graph of) an n-dimensional hypercube with its edges oriented so that every face has a unique sink. Such an orientation is called a unique sink orientation, and we are interested in finding the unique sink of the whole cube, when the orientation is given implicitly. The basic operation available is the so-called vertex evaluation, where we can access an arbitrary vert... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Lower bounds for polynomial calculus: non-binomial case

    Publication Year: 2001, Page(s):190 - 199
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (296 KB) | HTML iconHTML

    We generalize recent linear lower bounds for Polynomial Calculus based on binomial ideals. We produce a general hardness criterion (that we call immunity) which is satisfied by a random function and prove linear lower bounds on the degree of PC refutations for a wide class of tautologies based on immune functions. As some applications of our techniques, we introduce modp Tseitin tautolo... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Expander-based constructions of efficiently decodable codes

    Publication Year: 2001, Page(s):658 - 667
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (280 KB) | HTML iconHTML

    We present several novel constructions of codes which share the common thread of using expander (or expander-like) graphs as a component. The expanders enable the design of efficient decoding algorithms that correct a large number of errors through various forms of "voting" procedures. We consider both the notions of unique and list decoding, and in all cases obtain asymptotically good codes which... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Informational complexity and the direct sum problem for simultaneous message complexity

    Publication Year: 2001, Page(s):270 - 278
    Cited by:  Papers (62)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (248 KB) | HTML iconHTML

    Given m copies of the same problem, does it take m times the amount of resources to solve these m problems? This is the direct sum problem, a fundamental question that has been studied in many computational models. We study this question in the simultaneous message (SM) model of communication introduced by A.C. Yao (1979). The equality problem for n-bit strings is well known to have SM complexity ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Tight approximation results for general covering integer programs

    Publication Year: 2001, Page(s):522 - 528
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (200 KB) | HTML iconHTML

    In this paper we study approximation algorithms for solving a general covering integer program. An n-vector x of nonnegative integers is sought, which minimizes cT·x, subject to Ax≥b, x≤d. The entries of A, b, c are nonnegative. Let m be the number of rows of A. Covering problems have been heavily studied in combinatorial optimization. We focus on the effect of the multipli... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Testing random variables for independence and identity

    Publication Year: 2001, Page(s):442 - 451
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (240 KB) | HTML iconHTML

    Given access to independent samples of a distribution A over [n] × [m], we show how to test whether the distributions formed by projecting A to each coordinate are independent, i.e., whether A is ε-close in the L1 norm to the product distribution A1×A2 for some distributions A1 over [n] and A2 over [m]. The sample complexity o... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Universally composable security: a new paradigm for cryptographic protocols

    Publication Year: 2001, Page(s):136 - 145
    Cited by:  Papers (248)  |  Patents (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (232 KB) | HTML iconHTML

    We propose a novel paradigm for defining security of cryptographic protocols, called universally composable security. The salient property of universally composable definitions of security is that they guarantee security even when a secure protocol is composed of an arbitrary set of protocols, or more generally when the protocol is used as a component of an arbitrary system. This is an essential p... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The complexity of factors of multivariate polynomials

    Publication Year: 2001, Page(s):378 - 385
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (224 KB) | HTML iconHTML

    The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such families of polynomial functions of p-bounded degree overfields of characteristic zero. The proof relies on a polynomial upper bound on the approximative complex... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.