44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.

11-14 Oct. 2003

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Displaying Results 1 - 25 of 66
  • Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs

    Publication Year: 2003, Page(s):56 - 65
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (537 KB) | HTML iconHTML

    A directed multigraph is said to be d-regular if the indegree and outdegree of every vertex is exactly d. By Hall's theorem one can represent such a multigraph as a combination of at most n2 cycle covers each taken with an appropriate multiplicity. We prove that if the d-regular multigraph does not contain more than └d/2 View full abstract»

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  • Approximation algorithms for orienteering and discounted-reward TSP

    Publication Year: 2003, Page(s):46 - 55
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (331 KB) | HTML iconHTML

    In this paper, we give the first constant-factor approximation algorithm for the rooted orienteering problem, as well as a new problem that we call the Discounted-Reward TSP, motivated by robot navigation. In both problems, we are given a graph with lengths on edges and prizes (rewards) on nodes, and a start node s. In the orienteering problem, the goal is to find a path that maximizes the reward ... View full abstract»

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  • Quantum search of spatial regions

    Publication Year: 2003, Page(s):200 - 209
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1040 KB) | HTML iconHTML

    Can Grover's quantum search algorithm speed up search of a physical region - for example a 2D grid of size √n x √n? The problem is that √n time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a d-dimensional hypercube in ti... View full abstract»

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  • Symmetric polynomials over Zm and simultaneous communication protocols

    Publication Year: 2003, Page(s):450 - 459
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (560 KB) | HTML iconHTML

    We study the problem of representing symmetric Boolean functions as symmetric polynomials over Zm. We show an equivalence between such representations and simultaneous communication protocols. Computing a function f on 0 - 1 inputs with a polynomial of degree d modulo pq is equivalent to a two player simultaneous protocol for computing f where one player is given the first [logp View full abstract»

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  • Paths, trees, and minimum latency tours

    Publication Year: 2003, Page(s):36 - 45
    Cited by:  Papers (28)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (351 KB) | HTML iconHTML

    We give improved approximation algorithms for a variety of latency minimization problems. In particular, we give a 3.59-approximation to the minimum latency problem, improving on previous algorithms by a multiplicative factor of 2. Our techniques also give similar improvements for related problems like k-traveling repairmen and its multiple depot variant. We also observe that standard techniques c... View full abstract»

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  • Instability of FIFO at arbitrarily low rates in the adversarial queuing model

    Publication Year: 2003, Page(s):160 - 167
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (344 KB) | HTML iconHTML

    We study the stability of the commonly used packet forwarding protocol, FIFO (First In First Out), in the adversarial queuing model. We prove that FIFO can become unstable, i.e., lead to unbounded buffer-occupancies and queuing delays, at arbitrarily low injection rates. In order to demonstrate instability at rate r, we use a network of size polynomial in 1/r. View full abstract»

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  • Learning DNF from random walks

    Publication Year: 2003, Page(s):189 - 198
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (341 KB) | HTML iconHTML

    We consider a model of learning Boolean functions from examples generated by a uniform random walk on {0, 1}n. We give a polynomial time algorithm for learning decision trees and DNF formulas in this model. This is the first efficient algorithm for learning these classes in a natural passive learning model where the learner has no influence over the choice of examples used for learning. View full abstract»

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  • A group-theoretic approach to fast matrix multiplication

    Publication Year: 2003, Page(s):438 - 449
    Cited by:  Papers (17)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (675 KB) | HTML iconHTML

    We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group algebra C[G], and (2) controlling the dimensions of the irreducible representations of such groups. We present machinery and examples to support (1), including... View full abstract»

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  • Lower bounds for non-black-box zero knowledge

    Publication Year: 2003, Page(s):384 - 393
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (323 KB) | HTML iconHTML

    We show new lower bounds and impossibility results for general (possibly non-black-box) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a constant-round zero-knowledge strong proof (or argument) of knowledge (as defined by Goldreich, 2001) for a nontrivial language; 2. There does not exist a two-round zero-knowledge p... View full abstract»

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  • Logconcave functions: geometry and efficient sampling algorithms

    Publication Year: 2003, Page(s):640 - 649
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (534 KB) | HTML iconHTML

    The class of logconcave functions in Rn is a common generalization of Gaussians and of indicator functions of convex sets. Motivated by the problem of sampling from a logconcave density function, we study their geometry and introduce an analysis technique for "smoothing" them out. This leads to efficient sampling algorithms with no assumptions on the local smoothness of the density func... View full abstract»

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  • On certain connectivity properties of the Internet topology

    Publication Year: 2003, Page(s):28 - 35
    Cited by:  Papers (16)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (433 KB) | HTML iconHTML

    We show that random graphs in the preferential connectivity model have constant conductance, and hence have worst-case routing congestion that scales logarithmically with the number of nodes. Another immediate implication is constant spectral gap between the first and second eigenvalues of the random walk matrix associated with these graphs. We also show that the expected frugality (overpayment in... View full abstract»

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  • Proving hard-core predicates using list decoding

    Publication Year: 2003, Page(s):146 - 157
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1117 KB) | HTML iconHTML

    We introduce a unifying framework for proving that predicate P is hard-core for a one-way function f, and apply it to a broad family of functions and predicates, reproving old results in an entirely different way as well as showing new hard-core predicates for well known one-way function candidates. Our framework extends the list-coding method of Goldreich and Levin for showing hard-core predicate... View full abstract»

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  • Stability and efficiency of a random local load balancing protocol

    Publication Year: 2003, Page(s):472 - 481
    Cited by:  Papers (2)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (518 KB) | HTML iconHTML

    We study the long term (steady state) performance of a simple, randomized, local load balancing technique. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversary. The adversary knows the current and past load distribution in the network and can use this information to place the new tasks in the pro... View full abstract»

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  • Always Good Turing: asymptotically optimal probability estimation

    Publication Year: 2003, Page(s):179 - 188
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (814 KB) | HTML iconHTML

    While deciphering the German Enigma code during World War II, I.J. Good and A.M. Turing considered the problem of estimating a probability distribution from a sample of data. They derived a surprising and unintuitive formula that has since been used in a variety of applications and studied by a number of researchers. Borrowing an information-theoretic and machine-learning framework, we define the ... View full abstract»

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  • Bounded-concurrent secure two-party computation in a constant number of rounds

    Publication Year: 2003, Page(s):404 - 413
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (340 KB) | HTML iconHTML

    We consider the problem of constructing a general protocol for secure two-party computation in a way that preserves security under concurrent composition. In our treatment, we focus on the case where an a-priori bound on the number of concurrent sessions is specified before the protocol is constructed. (a.k.a. bounded concurrency). We make no setup assumptions. Lindel (STOC 2003) has shown that an... View full abstract»

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  • Separating the power of monotone span programs over different fields

    Publication Year: 2003, Page(s):428 - 501
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (605 KB) | HTML iconHTML

    Monotone span programs are a linear-algebraic model of computation. They are equivalent to linear secret sharing schemes and have various applications in cryptography and complexity. A fundamental question is how the choice of the field in which the algebraic operations are performed effects the power of the span program. In this paper we prove that the power of monotone span programs over finite ... View full abstract»

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  • Rank bounds and integrality gaps for cutting planes procedures

    Publication Year: 2003, Page(s):318 - 327
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (415 KB) | HTML iconHTML

    We present a new method for proving rank lower bounds for Cutting Planes (CP) and several procedures based on lifting due to Lovasz and Schrijver (LS), when viewed as proof systems for unsatisfiability. We apply this method to obtain the following new results: first, we prove near-optimal rank bounds for Cutting Planes and Lovasz-Schrijver proofs for several prominent unsatisfiable CNF examples, i... View full abstract»

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  • More on average case vs approximation complexity

    Publication Year: 2003, Page(s):298 - 307
    Cited by:  Papers (32)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (342 KB) | HTML iconHTML

    We consider the problem to determine the maximal number of satisfiable equations in a linear system chosen at random. We make several plausible conjectures about the average case hardness of this problem for some natural distributions on the instances, and relate them to several interesting questions in the theory of approximation algorithms and in cryptography. Namely we show that our conjectures... View full abstract»

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  • Logics for reasoning about cryptographic constructions

    Publication Year: 2003, Page(s):372 - 383
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (580 KB) | HTML iconHTML

    We present two logical systems for reasoning about cryptographic constructions which are sound with respect to standard cryptographic definitions of security. Soundness of the first system is proved using techniques from nonstandard models of arithmetic. Soundness of the second system is proved by an interpretation into the first system. We also present examples of how these systems may be used to... View full abstract»

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  • Tight lower bounds for the distinct elements problem

    Publication Year: 2003, Page(s):283 - 288
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (292 KB) | HTML iconHTML

    We prove strong lower bounds for the space complexity of (ε, δ)-approximating the number of distinct elements F0 in a data stream. Let m be the size of the universe from which the stream elements are drawn. We show that any one-pass streaming algorithm for (ε, δ)-approximating F0 must use Ω(1/ε2) space when ε = Ω(m-1... View full abstract»

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  • On levels in arrangements of curves. II. A simple inequality and its consequences

    Publication Year: 2003, Page(s):544 - 550
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (370 KB) | HTML iconHTML

    We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the k-level has subquadratic (O(n2-12s/)) complexity. This answers one of the main open problems from the author's previous paper, which provided a weaker bound for a restricted class of curves (graphs of degree-s polynomials) only. When combined ... View full abstract»

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  • The Ising model on trees: boundary conditions and mixing time

    Publication Year: 2003, Page(s):628 - 639
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (723 KB) | HTML iconHTML

    We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics for the Ising model. Specifically, we show that the mixing time on an n-vertex regular tree with (+) boundary remains O(n log n) at all temperatures (in contrast to the free boundary case, where the mixing time is not bounded by any fixed polynomial at low temperatures). We also... View full abstract»

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  • Polynomial degree vs. quantum query complexity

    Publication Year: 2003, Page(s):230 - 239
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (346 KB) | HTML iconHTML

    The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function with polynomial degree M and quantum query complexity (M1.321...). This is the first superlinear ... View full abstract»

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  • Linear upper bounds for random walk on small density random 3-CNFs

    Publication Year: 2003, Page(s):352 - 361
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (549 KB) | HTML iconHTML

    We analyze the efficiency of the random walk algorithm on random 3-CNF instances, and prove linear upper bounds on the running time of this algorithm for small clause density, less than 1.63. Our upper bound matches the observed running time to within a multiplicative factor. This is the first sub-exponential upper bound on the running time of a local improvement algorithm on random instances. Our... View full abstract»

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  • I/O-efficient strong connectivity and depth-first search for directed planar graphs

    Publication Year: 2003, Page(s):261 - 270
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (342 KB) | HTML iconHTML

    We present the first I/O-efficient algorithms for the following fundamental problems on directed planar graphs: finding the strongly connected components, finding a simple-path 2/3-separator, and computing a depth-first spanning (DFS) tree. Our algorithms for the first two problems perform O(sort(N)) I/Os, where N = V + E and sort(N) = Θ((N/B)) is the number of I/Os required to sort N elemen... View full abstract»

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