Proceedings 41st Annual Symposium on Foundations of Computer Science

12-14 Nov. 2000

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  • Proceedings 41st Annual Symposium on Foundations of Computer Science

    Publication Year: 2000
    Request permission for commercial reuse | PDF file iconPDF (259 KB)
    Freely Available from IEEE
  • Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors

    Publication Year: 2000, Page(s):3 - 13
    Cited by:  Papers (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1060 KB)

    The main contribution is a new type of graph product, which we call the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constant-degree expanders of every size, starting from one constant-... View full abstract»

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  • Universality and tolerance

    Publication Year: 2000, Page(s):14 - 21
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (761 KB)

    For any positive integers r and n, let H(r,n) denote the family of graphs on n vertices with maximum degree r, and let H(r,n,n) denote the family of bipartite graphs H on 2n vertices with n vertices in each vertex class, and with maximum degree r. On one hand, we note that any H(r,n)-universal graph must have /spl Omega/(n/sup 2-2/r/) edges. On the other hand, for any n/spl ges/n/sub 0/(r), we exp... View full abstract»

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  • Extracting randomness via repeated condensing

    Publication Year: 2000, Page(s):22 - 31
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (955 KB)

    On an input probability distribution with some (min-)entropy an extractor outputs a distribution with a (near) maximum entropy rate (namely the uniform distribution). A natural weakening of this concept is a condenser, whose output distribution has a higher entropy rate than the input distribution (without losing much of the initial entropy). We construct efficient explicit condensers. The condens... View full abstract»

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  • Extracting randomness from samplable distributions

    Publication Year: 2000, Page(s):32 - 42
    Cited by:  Papers (51)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1107 KB)

    The standard notion of a randomness extractor is a procedure which converts any weak source of randomness into an almost uniform distribution. The conversion necessarily uses a small amount of pure randomness, which can be eliminated by complete enumeration in some, but not all, applications. We consider the problem of deterministically converting a weak source of randomness into an almost uniform... View full abstract»

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  • Pseudorandom generators in propositional proof complexity

    Publication Year: 2000, Page(s):43 - 53
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1021 KB)

    We call a pseudorandom generator G/sub n/:{0,1}/sup n//spl rarr/{0,1}/sup m/ hard for a propositional proof system P if P can not efficiently prove the (properly encoded) statement G/sub n/(x/sub 1/,...,x/sub n/)/spl ne/b for any string b/spl epsiv/{0,1}/sup m/. We consider a variety of "combinatorial" pseudorandom generators inspired by the Nisan-Wigderson generator on one hand, and by the constr... View full abstract»

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  • Stochastic models for the Web graph

    Publication Year: 2000, Page(s):57 - 65
    Cited by:  Papers (114)  |  Patents (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (779 KB)

    The Web may be viewed as a directed graph each of whose vertices is a static HTML Web page, and each of whose edges corresponds to a hyperlink from one Web page to another. We propose and analyze random graph models inspired by a series of empirical observations on the Web. Our graph models differ from the traditional G/sub n,p/ models in two ways: 1. Independently chosen edges do not result in th... View full abstract»

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  • Optimization problems in congestion control

    Publication Year: 2000, Page(s):66 - 74
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (806 KB)

    One of the crucial elements in the Internet's success is its ability to adequately control congestion. The paper defines and solves several optimization problems related to Internet congestion control, as a step toward understanding the virtues of the TCP congestion control algorithm currently used and comparing it with alternative algorithms. We focus on regulating the rate of a single unicast fl... View full abstract»

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  • Fairness measures for resource allocation

    Publication Year: 2000, Page(s):75 - 85
    Cited by:  Papers (19)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1110 KB)

    In many optimization problems, one seeks to allocate a limited set of resources to a set of individuals with demands. Thus, such allocations can naturally be viewed as vectors, with one coordinate representing each individual. Motivated by work in network routing and bandwidth assignment, we consider the problem of producing solutions that simultaneously approximate all feasible allocations in a c... View full abstract»

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  • On the approximability of trade-offs and optimal access of Web sources

    Publication Year: 2000, Page(s):86 - 92
    Cited by:  Papers (80)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (702 KB)

    We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that /spl epsiv/-approximates the Pareto curve, for any... View full abstract»

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  • How bad is selfish routing?

    Publication Year: 2000, Page(s):93 - 102
    Cited by:  Papers (63)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (926 KB)

    We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route traffic such that the sum of all travel times-the total latency-is minimized. In many settings, includ... View full abstract»

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  • A polylogarithmic approximation of the minimum bisection

    Publication Year: 2000, Page(s):105 - 115
    Cited by:  Papers (11)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1086 KB)

    A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size n/2. The bisection cost is the number of edges connecting the two sets. Finding the bisection of minimum cost is NP-hard. We present an algorithm that finds a bisection whose cost is within ratio of O(log/sup 2/ n) from the optimal. For graphs excluding any fixed graph as a minor (e.g. planar graphs) ... View full abstract»

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  • Approximability and in-approximability results for no-wait shop scheduling

    Publication Year: 2000, Page(s):116 - 125
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (987 KB)

    We investigate the approximability of no-wait shop scheduling problems under the makespan criterion. In a flow shop, all jobs pass through the machines in the same ordering. In the more general job shop, the routes of the jobs are job-dependent. We present a polynomial time approximation scheme (PTAS) for the no-wait flow shop problem on any fixed number of machines. Unless P=NP, this result canno... View full abstract»

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  • Nested graph dissection and approximation algorithms

    Publication Year: 2000, Page(s):126 - 135
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (977 KB)

    This paper considers approximation algorithms for graph completion problems using the nested dissection paradigm. Given a super-additive function of interest (the smallest planar or chordal extension for example) and a test that relates it to an upper bound of the smallest separator, we provide a framework how to dissect the graph recursively such that no subgraph has more than half the value of i... View full abstract»

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  • Approximating the single source unsplittable min-cost flow problem

    Publication Year: 2000, Page(s):136 - 145
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (981 KB)

    In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path and the total cost must not exceed a given budget. This problem has been introduced by J.M. Kleinberg (1996) and generalizes sev... View full abstract»

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  • Hardness of approximate hypergraph coloring

    Publication Year: 2000, Page(s):149 - 158
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (998 KB)

    We introduce the notion of covering complexity of a probabilistic verifier. The covering complexity of a verifier on a given input is the minimum number of proofs needed to "satisfy" the verifier on every random string, i.e., on every random string, at least one of the given proofs must be accepted by the verifier. The covering complexity of PCP verifiers offers a promising route to getting strong... View full abstract»

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  • "Soft-decision" decoding of Chinese remainder codes

    Publication Year: 2000, Page(s):159 - 168
    Cited by:  Papers (21)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (992 KB)

    Given n relatively prime integers p/sub 1/<...<p/sub n/ and an integer k<n, the Chinese Remainder Code, CRT/sub p1,...,pnik/, has as its message space M={0,...,/spl Pi//sub i=1//sup k/,pi-1}, and encodes a message m /spl isin/M as the vector <m/sub 1/,...,m/sub n/>, where m/sub i/=m(mod p/sub i/). The soft-decision decoding problem for the Chinese remainder code is given as input a ... View full abstract»

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  • Super-linear time-space tradeoff lower bounds for randomized computation

    Publication Year: 2000, Page(s):169 - 179
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1090 KB)

    We prove the first time-space lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by M. Ajtai (1999) in his time-space tradeoffs for deterministic RAM algorithms computing element distinctness and for... View full abstract»

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  • On the hardness of graph isomorphism

    Publication Year: 2000, Page(s):180 - 186
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (625 KB)

    We show that the graph isomorphism problem is hard under logarithmic space many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space), for every logarithmic space modular class Mod/sub k/L and for the class DET of problems NC/sup 1/ reducible to the determinant. These are the strongest existing hardness results for the graph isomorphism problem, and imply a randomized ... View full abstract»

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  • Stable distributions, pseudorandom generators, embeddings and data stream computation

    Publication Year: 2000, Page(s):189 - 197
    Cited by:  Papers (48)  |  Patents (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (678 KB)

    In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: we show how to maintain (using only O(log n//spl epsiv//sup 2/) words of storage) a sketch C(p) of a point p/spl isin/l/sub 1//sup n/ under dynamic updates of its coordinates, such that given sketches C(p) and C(q) one can estimate |p-q|/sub 1/ ... View full abstract»

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  • New data structures for orthogonal range searching

    Publication Year: 2000, Page(s):198 - 207
    Cited by:  Papers (32)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (988 KB)

    We present new general techniques for static orthogonal range searching problems in two and higher dimensions. For the general range reporting problem in R/sup 3/, we achieve query time O(log n+k) using space O(n log/sup 1+/spl epsiv// n), where n denotes the number of stored points and k the number of points to be reported. For the range reporting problem on an n/spl times/n grid, we achieve quer... View full abstract»

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  • Nearly optimal expected-case planar point location

    Publication Year: 2000, Page(s):208 - 218
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1013 KB)

    We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which cell of the subdivision contains a given query point, so as to minimize the expected search time. Th... View full abstract»

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  • On levels in arrangements of curves

    Publication Year: 2000, Page(s):219 - 227
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (799 KB)

    Analyzing the worst-case complexity of the k-level in a planar arrangement of n curves is a fundamental problem in combinatorial geometry. We give the first subquadratic upper bound (roughly O(nk/sup 1-2/3/*)) for curves that are graphs of polynomial functions of an arbitrary fixed degree s. Previously, nontrivial results were known only for the case s=1 and s=2. We also improve the earlier bound ... View full abstract»

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  • Detecting a network failure

    Publication Year: 2000, Page(s):231 - 239
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (825 KB)

    Measuring the properties of a large, unstructured network can be difficult: one may not have full knowledge of the network topology, and detailed global measurements may be infeasible. A valuable approach to such problems is to take measurements from selected locations within the network and then aggregate them to infer large-scale properties. One sees this notion applied in settings that range fr... View full abstract»

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  • Testing of clustering

    Publication Year: 2000, Page(s):240 - 250
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1014 KB)

    A set X of points in /spl Rfr//sup d/ is (k,b)-clusterable if X can be partitioned into k subsets (clusters) so that the diameter (alternatively, the radius) of each cluster is at most b. We present algorithms that by sampling from a set X, distinguish between the case that X is (k,b)-clusterable and the case that X is /spl epsiv/-far from being (k,b')-clusterable for any given 0</spl epsiv//sp... View full abstract»

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