Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)

8-11 Nov. 1998

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  • Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)

    Publication Year: 1998
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    Freely Available from IEEE
  • Geometric computation and the art of sampling (tutorial)

    Publication Year: 1998, Page(s): 2
    Cited by:  Papers (2)
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  • A tutorial on theoretical issues in probabilistic artificial intelligence

    Publication Year: 1998, Page(s): 4
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  • Author index

    Publication Year: 1998, Page(s):744 - 745
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  • Informatin Retrieval on the Web

    Publication Year: 1998, Page(s): 6
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  • Local search in smooth convex sets

    Publication Year: 1998, Page(s):218 - 226
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    In this paper we analyse two very simple techniques to minimize a linear function over a convex set. The first is a deterministic algorithm based on gradient descent. The second is a randomized algorithm which makes a small local random change at every step. The second method can be used when the convex set is presented by just a membership oracle whereas the first requires something similar to a ... View full abstract»

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  • 1-way quantum finite automata: strengths, weaknesses and generalizations

    Publication Year: 1998, Page(s):332 - 341
    Cited by:  Papers (26)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (124 KB)

    We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversibl... View full abstract»

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  • Tseitin's tautologies and lower bounds for Nullstellensatz proofs

    Publication Year: 1998, Page(s):648 - 652
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (148 KB)

    We use the known linear lower bound for Tseitin's tautologies for establishing linear lower bounds on the degree of Nullstellensatz proofs (in the usual boolean setting) for explicitly constructed systems of polynomials of a constant (in our construction 6) degree. It holds over any field of characteristic distinct from 2. Previously, a linear lower bound was proved for an explicitly constructed s... View full abstract»

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  • Multiplicative complexity of Taylor shifts and a new twist of the substitution method

    Publication Year: 1998, Page(s):212 - 215
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (100 KB)

    Let Cn=Cn(K) denote the minimum number of essential multiplications/divisions required for shifting a general n-th degree polynomial A(t)=Σaiti to some new origin x, which means to compute the coefficients bk of the Taylor expansion A(x+t)=B(t)=Σbktk as elements of K(x,a0,...,an) with ind... View full abstract»

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  • Approximation of diameters: randomization doesn't help

    Publication Year: 1998, Page(s):244 - 251
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (136 KB)

    We describe a deterministic polynomial-time algorithm which, for a convex body K in Euclidean n-space, finds upper and lower bounds on K's diameter which differ by a factor of O(√n/logn). We show that this is, within a constant factor, the best approximation to the diameter that a polynomial-time algorithm can produce even if randomization is allowed. We also show that the above results hold... View full abstract»

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  • Optimal time-space trade-offs for sorting

    Publication Year: 1998, Page(s):264 - 268
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (92 KB)

    We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem. P. Beame (1991) has shown a lower bound of Ω(n2) for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of O(n2 log n) due to G.N. Frederickson (1987... View full abstract»

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  • On the single-source unsplittable flow problem

    Publication Year: 1998, Page(s):290 - 299
    Cited by:  Papers (9)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (172 KB)

    Let G=(V,E) be a capacitated directed graph with a source s and k terminals ti with demands di, 1⩽i⩽k. We would like to concurrently route every demand on a single path from s to the corresponding terminal without violating the capacities. There are several interesting and important variations of this unsplittable flow problem. If the necessary cut condition is satisf... View full abstract»

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  • Exponential separations between restricted resolution and cutting planes proof systems

    Publication Year: 1998, Page(s):638 - 647
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (184 KB)

    We prove an exponential lower bound for tree-like cutting planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between tree-like and dag-like proofs for both cutting planes and resolution; in both cases only superpolynomial separations were known before. In order to prove this, we extend the lower bounds on the depth of mon... View full abstract»

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  • Probabilistically checkable proofs with low amortized query complexity

    Publication Year: 1998, Page(s):18 - 27
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (168 KB)

    The error probability of Probabilistically Checkable Proof (PCP) systems can be made exponentially small in the number of queries by using sequential repetition. In this paper we are interested in determining the precise rate at which the error goes down in an optimal protocol, and we make substantial progress toward a tight resolution of this question. A PCP verifier uses q¯ amortized query ... View full abstract»

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  • Recommendation systems: a probabilistic analysis

    Publication Year: 1998, Page(s):664 - 673
    Cited by:  Papers (12)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (136 KB)

    A recommendation system tracks past actions of a group of users to make recommendations to individual members of the group. The growth of computer-mediated marketing and commerce has led to increased interest in such systems. We introduce a simple analytical framework for recommendation systems, including a basis for defining the utility of such a system. We perform probabilistic analyses of algor... View full abstract»

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  • The access network design problem

    Publication Year: 1998, Page(s):40 - 49
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (144 KB)

    We consider the problem of designing a minimum cost access network to carry traffic from a set of endnodes to a core network. A set of trunks of K differing types are available for leasing or buying. Some trunk-types have a high initial overhead cost but a low cost per unit bandwidth. Others have a low overhead cost but a high cost per unit bandwidth. When the central core is given, we show how to... View full abstract»

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  • A primitive recursive algorithm for the general Petri net reachability problem

    Publication Year: 1998, Page(s):130 - 136
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (120 KB)

    E. Mayr and R. Kosaraju (1981) proved the decidability of the general Petri net reachability problem. However their algorithms are non primitive recursive. Since then the primitive recursiveness of this problem was stated as an open problem. In this paper we give a double exponential space algorithm for the general Petri net reachability problem View full abstract»

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  • Satisfiability of word equations with constants is in exponential space

    Publication Year: 1998, Page(s):112 - 119
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (124 KB)

    In this paper we study solvability of equations over free semigroups, known as word equations, particularly G.S. Makanin's algorithm (1977), a general procedure to decide if a word equation has a solution. The upper bound time-complexity of Makanin's original decision procedure was quadruple exponential in the length of the equation, as shown by Jaffar. A. Koscielski and L. Pacholski (1996) reduce... View full abstract»

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  • The shortest vector in a lattice is hard to approximate to within some constant

    Publication Year: 1998, Page(s):92 - 98
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (140 KB)

    We show the shortest vector problem in the l2 norm is NP-hard (for randomized reductions) to approximate within any constant factor less than √2. We also give a deterministic reduction under a reasonable number theoretic conjecture. Analogous results hold in any lp norm (p⩾1). In proving our NP-hardness result, we give an alternative construction satisfying Ajtai's ... View full abstract»

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  • Orchestrating quartets: approximation and data correction

    Publication Year: 1998, Page(s):416 - 425
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (152 KB)

    Inferring evolutionary trees has long been a challenging problem both for biologists and computer scientists. In recent years research has concentrated on the quartet method paradigm for inferring evolutionary trees. Quartet methods proceed by first inferring the evolutionary history for every set of four species (resulting in a set Q of inferred quarter topologies) and then recombining these infe... View full abstract»

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  • Unsatisfiable systems of equations, over a finite field

    Publication Year: 1998, Page(s):202 - 211
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (156 KB)

    The properties of any system of k simultaneous equations in n variables over GF(q), are studied, with a particular emphasis on unsatisfiable systems. A general formula for the number of solutions is given, which can actually be useful for computing that number in the special case where all the equations are of degree 2. When such a quadratic system has no solution, there is always a proof of unsat... View full abstract»

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  • A linguistic characterization of bounded oracle computation and probabilistic polynomial time

    Publication Year: 1998, Page(s):725 - 733
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (140 KB)

    We present a higher-order functional notation for polynomial-time computation with an arbitrary 0, 1-valued oracle. This formulation provides a linguistic characterization for classes such as NP and BPP, as well as a notation for probabilistic polynomial-time functions. The language is derived from Hofmann's adaptation of Bellantoni-Cook safe recursion, extended to oracle computation via work deri... View full abstract»

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  • Perfect information leader election in log*n+O(1) rounds

    Publication Year: 1998, Page(s):576 - 583
    Cited by:  Papers (6)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (124 KB)

    In the leader election problem, n players wish to elect a random leader. The difficulty is that some coalition of players may conspire to elect one of its own members. We adopt the perfect information model: all communication is by broadcast, and the bad players have unlimited computational power. Within a round, they may also wait to see the inputs of the good players. A protocol is called resili... View full abstract»

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  • Lower bounds for zero knowledge on the Internet

    Publication Year: 1998, Page(s):484 - 492
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (148 KB)

    We consider zero knowledge interactive proofs in a richer, more realistic communication environment. In this setting, one may simultaneously engage in many interactive proofs, and these proofs may take place in an asynchronous fashion. It is known that zero-knowledge is not necessarily preserved in such an environment; we show that for a large class of protocols, it cannot be preserved. Any 4 roun... View full abstract»

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  • Fast Monte-Carlo algorithms for finding low-rank approximations

    Publication Year: 1998, Page(s):370 - 378
    Cited by:  Papers (42)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (120 KB)

    In several applications, the data consists of an m×n matrix A and it is of interest to find an approximation D of a specified rank k to A where, k is much smaller than m and n. Traditional methods like the Singular Value Decomposition (SVD) help us find the “best” such approximation. However, these methods take time polynomial in m, n which is often too prohibitive. In this paper... View full abstract»

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