Proceedings 35th Annual Symposium on Foundations of Computer Science

20-22 Nov. 1994

Filter Results

Displaying Results 1 - 25 of 74
  • Proceedings 35th Annual Symposium on Foundations of Computer Science

    Publication Year: 1994
    Request permission for commercial reuse | |PDF file iconPDF (87 KB)
    Freely Available from IEEE
  • Expander codes

    Publication Year: 1994, Page(s):566 - 576
    Cited by:  Papers (9)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (776 KB)

    We present a new class of asymptotically good, linear error-correcting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both randomized and explicit constructions for some of these codes. Experimental results demonstrate the extrem... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Efficient average-case algorithms for the modular group

    Publication Year: 1994, Page(s):143 - 152
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (648 KB)

    The modular group occupies a central position in many branches of mathematical sciences. In this paper we give average polynomial-time algorithms for the unbounded and bounded membership problems for finitely generated subgroups of the modular group. The latter result affirms a conjecture of Y. Gurevich (1990) View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • The geometry of graphs and some of its algorithmic applications

    Publication Year: 1994, Page(s):577 - 591
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1084 KB)

    We explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an atte... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Algebraic computation trees in characteristic p>0

    Publication Year: 1994, Page(s):534 - 539
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (392 KB)

    We provide a simple and powerful combinatorial method for proving lower bounds for algebraic computation trees over algebraically closed fields of characteristic p>0. We apply our method to prove, for example, an Ω(n log n) lower bound for the n element distinctness problem, an Ω(n log(n/k)) lower bound to the “k-equal problem”-that is deciding whether there are k identi... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Finding the k shortest paths

    Publication Year: 1994, Page(s):154 - 165
    Cited by:  Papers (120)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (904 KB)

    We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m+n log n+k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m+n log n+kn). We describe applications t... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Tail bounds for occupancy and the satisfiability threshold conjecture

    Publication Year: 1994, Page(s):592 - 603
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (828 KB)

    The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the following well-known conjecture on threshold p... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • An O(n1+ϵ log b) algorithm for the complex roots problem

    Publication Year: 1994, Page(s):540 - 547
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (524 KB)

    Given a univariate polynomial f(z) of degree n with complex coefficients, whose real and imaginary parts can be expressed as a ratio of two integers less than 2m in magnitude, the root problem is to find all the roots of f(z) up to specified precision 2-μ . Assuming the arithmetic model for computation, we provide, for any ε>0, an algorithm which has complexity O(n... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Maximum agreement subtree in a set of evolutionary trees-metrics and efficient algorithms

    Publication Year: 1994, Page(s):758 - 769
    Cited by:  Papers (3)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (820 KB)

    In this paper we prove that the maximum homeomorphic agreement subtree problem is 𝒩𝒫-complete for three trees with unbounded degrees. We then show an approximation algorithm of time O(kn5) for choosing the species that are not in a maximum agreement subtree of a set of k trees. Our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution. ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • “Go with the winners” algorithms

    Publication Year: 1994, Page(s):492 - 501
    Cited by:  Papers (15)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (620 KB)

    We can view certain randomized optimization algorithms as rules for randomly moving a particle around in a state space; each state might correspond to a distinct solution to the optimization problem, or more generally, the state space might express some other structure underlying the optimization algorithm. In this setting, a general paradigm for designing heuristics is to run several simulations ... View full abstract»

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

    Publication Year: 1994, Page(s):436 - 453
    Cited by:  Papers (27)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1408 KB)

    This paper puts forward a computationally-based notion of proof and explores its implications to computation at large. In particular, given a random oracle or a suitable cryptographic assumption, we show that every computation possesses a short certificate vouching its correctness, and that, under a cryptographic assumption, any program for a 𝒩𝒫-complete problem is checkable in polynomia... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Lower bounds on Hilbert's Nullstellensatz and propositional proofs

    Publication Year: 1994, Page(s):794 - 806
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (916 KB)

    The weak form of the Hilbert's Nullstellensatz says that a system of algebraic equations over a field, Qi(x¯)=0, does not have a solution in the algebraic closure iff 1 is in the ideal generated by the polynomials Qi(x¯). We shall prove a lower bound on the degrees of polynomials Pi(x¯) such that Σ i Pi(x¯)Qi View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Long tours and short superstrings

    Publication Year: 1994, Page(s):166 - 177
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (900 KB)

    This paper considers weight-maximizing variants of the classical symmetric and asymmetric traveling-salesman problems. Like their weight-minimizing counterparts, these variants are MAX SNP-hard. We present the first nontrivial approximation algorithms for these problems. Our algorithm for directed graphs finds a tour whose weight is at least 38/63≈0.603 times the weight of a maximum-weight tour... View full abstract»

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

    Publication Year: 1994, Page(s):604 - 612
    Cited by:  Papers (31)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (644 KB)

    We introduce a novel approach for sending messages over lossy packet-based networks. The new method, called Priority Encoding Transmission, allows a user to specify a different priority on each segment of the message. Based on the priorities, the sender uses the system to encode the segments into packets for transmission. The system ensures recovery of the segments in order of their priority. The ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Efficient oblivious branching programs for threshold functions

    Publication Year: 1994, Page(s):309 - 317
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (556 KB)

    In his survey paper on branching programs, A.A. Razborov (1991) asked the following question: Does every rectifier-switching network computing the majority of n bits have size n1+Ω(1)? We answer this question in the negative by constructing a simple oblivious branching program of size O(n log3 n/log log n log log log n) for computing any threshold function. This improve... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Complexity lower bounds for computation trees with elementary transcendental function gates

    Publication Year: 1994, Page(s):548 - 552
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (348 KB)

    We consider computation trees which admit as gate functions along with the usual arithmetic operations also algebraic or transcendental functions like exp, log, sin, square root (defined in the relevant domains) or much more general, Pfaffian functions. A new method for proving lower bounds on the depth of these trees is developed which allows to prove a lower bound Ω(√(log N)) for tes... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Optimal evolutionary tree comparison by sparse dynamic programming

    Publication Year: 1994, Page(s):770 - 779
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (796 KB)

    In computational biology one is often interested in finding the concensus between different evolutionary trees for the same set of species. A popular formalizations is the Maximum Agreement Subtree Problem (MAST) defined as follows: given a set A and two rooted trees 𝒯0 and 𝒯1 leaf-labeled by the elements of A, find a maximum cardinality subset B of A such that the ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On the robustness of functional equations

    Publication Year: 1994, Page(s):288 - 299
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (884 KB)

    Given a functional equation, such as ∀x, y f(x)+f(y)=f(x+y), we study the following general question: When can the “for all” quantifiers be replaced by “for most” quantifiers without essentially changing the functions that are characterized by the property? When “for most” quantifiers are sufficient, we say that the functional equation is robust. We show ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Computing with very weak random sources

    Publication Year: 1994, Page(s):264 - 275
    Cited by:  Papers (8)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (904 KB)

    For any fixed ε>0, we show how to simulate RP algorithms in time nO(log n) using the output of a δ-source with min-entropy R(ε). Such a weak random source is asked once for R(ε) bits; it outputs an R-bit string such that any string has probability at most 2-R(ε). If ε>1-1/(k+1), our BPP simulations take time nO(log(k n)) (log View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A spectral approach to lower bounds

    Publication Year: 1994, Page(s):674 - 682
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (584 KB)

    We establish a nonlinear lower bound for halfplane range searching over a group. Specifically, we show that summing up the weights of n (weighted) points within n halfplanes requires Ω(n log n) additions and subtractions. This is the first nontrivial lower bound for range searching over a group. By constrast, range searching over a semigroup (which forbids subtractions) is almost completely ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • More output-sensitive geometric algorithms

    Publication Year: 1994, Page(s):695 - 702
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (572 KB)

    A simple idea for speeding up the computation of extrema of a partially ordered set turns out to have a number of interesting applications in geometric algorithms; the resulting algorithms generally replace an appearance of the input size n in the running time by an output size A⩽n. In particular, the A coordinate-wise minima of a set of n points in Rd can be found by an algorithm n... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Finding separator cuts in planar graphs within twice the optimal

    Publication Year: 1994, Page(s):14 - 23
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (660 KB)

    Building on the works of S.B. Rao (1987, 1992) and J.K. Park and C.A. Phillips (1993), we present a factor 2 approximation algorithm for the problem of finding a minimum cost b-balanced cut in planar graphs, for b⩽1/3, if the vertex weights are given in unary (using scaling, a psuedo-approximation algorithm is also presented for the case of binary vertex weights). This problem is of considerab... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Randomized simplex algorithms on Klee-Minty cubes

    Publication Year: 1994, Page(s):502 - 510
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (612 KB)

    We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes (1972) and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random ... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • On monotone formula closure of SZK

    Publication Year: 1994, Page(s):454 - 465
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (940 KB)

    We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the non-interactive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that interactive SZK for random self reducible languages (RSR) (and for co-RSR) is closed under monotone B... View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Fast and lean self-stabilizing asynchronous protocols

    Publication Year: 1994, Page(s):226 - 239
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (1084 KB)

    We consider asynchronous general topology dynamic networks of identical nameless nodes with worst-case transient faults. Starting from any faulty configuration, our protocols self-stabilize any computation in time polynomial in the (unknown) network diameter. This version sacrifices some diversity of tasks and efficiency for simplicity and clarity of details. Appendix gives more efficient procedur... View full abstract»

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