Proceedings of 37th Conference on Foundations of Computer Science

14-16 Oct. 1996

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  • Proceedings of 37th Conference on Foundations of Computer Science

    Publication Year: 1996
    Request permission for commercial reuse | PDF file iconPDF (355 KB)
    Freely Available from IEEE
  • Polynomial time approximation schemes for Euclidean TSP and other geometric problems

    Publication Year: 1996, Page(s):2 - 11
    Cited by:  Papers (53)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1054 KB)

    We present a polynomial time approximation scheme for Euclidean TSP in /spl Rfr//sup 2/. Given any n nodes in the plane and /spl epsiv/>0, the scheme finds a (1+/spl epsiv/)-approximation to the optimum traveling salesman tour in time n/sup 0(1//spl epsiv/)/. When the nodes are in /spl Rfr//sup d/, the running time increases to n(O/spl tilde/(log/sup d-2/n)//spl epsiv//sup d-1/) The previous be... View full abstract»

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  • The regularity lemma and approximation schemes for dense problems

    Publication Year: 1996, Page(s):12 - 20
    Cited by:  Papers (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (660 KB)

    There are two main contributions of the present paper. In the first, we use the constructive version of the Regularity Lemma to give directly simple polynomial time approximation schemes for several graph "subdivision" problems in dense graphs including the Max Cut problem, the Graph Bisection problem, the Min l-way cut problem and Graph Separator problem. Arora, Karger and Karpinski (1992) gave t... View full abstract»

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  • A new rounding procedure for the assignment problem with applications to dense graph arrangement problems

    Publication Year: 1996, Page(s):21 - 30
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (977 KB)

    We present a randomized procedure for rounding fractional perfect matchings to (integral) matchings. If the original fractional matching satisfies any linear inequality, then with high probability, the new matching satisfies that linear inequality in an approximate sense. This extends the well-known LP rounding procedure of Raghavan and Thompson (1987), which is usually used to round fractional so... View full abstract»

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  • Approximate strip packing

    Publication Year: 1996, Page(s):31 - 36
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (564 KB)

    We present an approximation scheme for strip-packing, or packing rectangles into a rectangle of fixed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm finds a packing of n rectangles whose total height is within a factor of (1+/spl epsiv/) of optimal, and has running time polynomial both in n and in 1//spl epsiv/. It is based on a reduction to fractional bin-packi... View full abstract»

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  • A decision procedure for unitary linear quantum cellular automata

    Publication Year: 1996, Page(s):38 - 45
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (690 KB)

    Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution operator has to be a unitary transformation. In this paper we give an efficient algorithm to decide if a linear quantum cellular automaton is unitary. The comp... View full abstract»

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  • Polynomial simulations of decohered quantum computers

    Publication Year: 1996, Page(s):46 - 55
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1056 KB)

    Recently it has become clear, that a key issue in quantum computation is understanding how interaction with the environment, or "decoherence", affects the computational power of quantum computers. We adopt the standard physical method of describing systems which are interwound with their environment by "density matrices", and within this framework define a model of decoherence in quantum computati... View full abstract»

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  • Fault-tolerant quantum computation

    Publication Year: 1996, Page(s):56 - 65
    Cited by:  Papers (65)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1054 KB)

    It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer making long computations impossible. A further dif... View full abstract»

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  • Single-source unsplittable flow

    Publication Year: 1996, Page(s):68 - 77
    Cited by:  Papers (41)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1138 KB)

    The max-flow min-cut theorem of Ford and Fulkerson is based on an even more foundational result, namely Menger's theorem on graph connectivity Menger's theorem provides a good characterization for the following single-source disjoint paths problem: given a graph G, with a source vertex s and terminals t/sub 1/,...,t/sub k/, decide whether there exist edge-disjoint s-t/sub i/ paths for i=1,...,k. W... View full abstract»

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  • The optimal path-matching problem

    Publication Year: 1996, Page(s):78 - 85
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (819 KB)

    We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we present results implying the polynomial-time solvability of the two problems. We also use our results to give the first strongly polynomial separation algorithm for the convex hull of matchable sets of a graph, and the first polynomial-time algorithm to compute the... View full abstract»

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  • Short paths in expander graphs

    Publication Year: 1996, Page(s):86 - 95
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1038 KB)

    Graph expansion has proved to be a powerful general tool for analyzing the behavior of routing algorithms and the inter-connection networks on which they run. We develop new routing algorithms and structural results for bounded-degree expander graphs. Our results are unified by the fact that they are all based upon, and extend, a body of work: asserting that expanders are rich in short, disjoint p... View full abstract»

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  • Spectral partitioning works: planar graphs and finite element meshes

    Publication Year: 1996, Page(s):96 - 105
    Cited by:  Papers (30)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (923 KB)

    Spectral partitioning methods use the Fiedler vector-the eigenvector of the second-smallest eigenvalue of the Laplacian matrix-to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree plana... View full abstract»

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  • Computing permanents over fields of characteristic 3: where and why it becomes difficult

    Publication Year: 1996, Page(s):108 - 114
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (466 KB)

    In this paper we consider the complexity of computing permanents over fields of characteristic 3. We present a polynomial time algorithm for computing per(A) for a matrix A such that the rank rg(AA/sup T/-I)/spl les/1. On the other hand, we show that existence of a polynomial-time algorithm for computing per(A) for a matrix A such that rg(AA/sup T/-I)/spl ges/2 implies NP=R. As a byproduct we obta... View full abstract»

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  • Solving systems of polynomial congruences modulo a large prime

    Publication Year: 1996, Page(s):115 - 124
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1028 KB)

    We consider the following polynomial congruences problem: given a prime p, and a set of polynomials f/sub 1/,...,f/sub m//spl isin/F/sub p/[x/sub 1/,...,x/sub n/] of total degree at most d, solve the system f/sub 1/=...=f/sub m/=0 for solution(s) in F/sub p//sup n/. We give a randomized algorithm for the decision version of this problem. When the system has F/sub p/-rational solutions our algorith... View full abstract»

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  • Median selection requires (2+/spl epsiv/)n comparisons

    Publication Year: 1996, Page(s):125 - 134
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1001 KB)

    Improving a long standing result of Bent and John (1985), we obtain a (2+/spl epsiv/)n lower bound (for some fixed /spl epsiv/>0) on the number of comparisons required, in the worst case, for selecting the median of n elements. The new lower bound is obtained using a weight function that allows us to combine leaf counting and adversary arguments. View full abstract»

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  • Faster deterministic sorting and searching in linear space

    Publication Year: 1996, Page(s):135 - 141
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (575 KB)

    We present a significant improvement on linear space deterministic sorting and searching. On a unit-cost RAM with word size w, an ordered set of n w-bit keys (viewed as binary strings or integers) can be maintained in O(min{[/spl radic/(logn)][logn/logw+loglogn][logwloglogn]}) time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worst-case wh... View full abstract»

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  • An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups

    Publication Year: 1996, Page(s):144 - 153
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (947 KB)

    We present an efficient algorithm for computing the minimal trellis for a group code over a finite Abelian group, given a generator matrix for the code. We also show how to compute a succinct representation of the minimal trellis for such a code, and present algorithms that use this information to efficiently compute local descriptions of the minimal trellis. This extends the work of Kschischang a... View full abstract»

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  • Highly fault-tolerant parallel computation

    Publication Year: 1996, Page(s):154 - 163
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (995 KB)

    We re-introduce the coded model of fault-tolerant computation in which the input and output of a computational device are treated as words in an error-correcting code. A computational device correctly computes a function in the coded model if its input and output, once decoded, are a valid input and output of the function. In the coded model, it is reasonable to hope to simulate all computational ... View full abstract»

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  • Maximum likelihood decoding of Reed Solomon codes

    Publication Year: 1996, Page(s):164 - 172
    Cited by:  Papers (3)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (716 KB)

    We present a randomized algorithm which takes as input n distinct points {(x/sub i/,y/sub i/)}/sub i=1//sup n/ from F/spl times/F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable a of degree at most d which agree with the given set of points in at least t places (i.e., y/sub i/=f(x/sub i/) for at least t values of i), pro... View full abstract»

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  • New coding techniques for improved bandwidth utilization

    Publication Year: 1996, Page(s):173 - 182
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1050 KB)

    The introduction of parallel models that account for communication between processors has shown that interprocessor bandwidth is often the limiting factor in parallel computing. In this paper, we introduce a new coding technique for transmitting the XOR of carefully selected patterns of bits to be communicated which greatly reduces bandwidth requirements in some settings. This technique has broade... View full abstract»

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  • Probabilistic approximation of metric spaces and its algorithmic applications

    Publication Year: 1996, Page(s):184 - 193
    Cited by:  Papers (113)  |  Patents (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1019 KB)

    This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any, metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilistically-approximates another metric space. We prove that any metric space ca... View full abstract»

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  • Factoring graphs to bound mixing rates

    Publication Year: 1996, Page(s):194 - 203
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (798 KB)

    This paper develops a new technique for bounding the mixing rate of a Markov chain by decomposing the state space into factors. The first application is an efficient Monte Carlo Markov chain algorithm for generating random three-colorings of 2-dimensional lattice regions. This provides a rigorous tool for studying some properties of the 3-state Potts model and the ice model from statistical mechan... View full abstract»

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  • Sampling according to the multivariate normal density

    Publication Year: 1996, Page(s):204 - 212
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (760 KB)

    This paper deals with the normal density of n dependent random variables. This is a function of the form: ce(-x/sup T/Ax) where A is an n/spl times/n positive definite matrix, a: is the n-vector of the random variables and c is a suitable constant. The first problem we consider is the (approximate) evaluation of the integral of this function over the positive orthant /spl int/(x/sub 1/=0)/sup /spl... View full abstract»

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  • Load balancing and density dependent jump Markov processes

    Publication Year: 1996, Page(s):213 - 222
    Cited by:  Papers (20)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1044 KB)

    We provide a new approach for analyzing both static and dynamic randomized load balancing strategies. We demonstrate the approach by providing the first analysis of the following model: customers arrive as a Poisson stream of rate /spl lambda//sub n/, /spl lambda/<1, at a collection of n servers. Each customer chooses some constant d servers independently and uniformly at random from the n serv... View full abstract»

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  • Tree data structures for N-body simulation

    Publication Year: 1996, Page(s):224 - 233
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (926 KB)

    In this paper, we study data structures for use in N-body simulation. We concentrate on the spatial decomposition tree used in particle-cluster force evaluation algorithms such as the Barnes-Hut algorithm. We prove that a k-d tree is asymptotically inferior to a spatially balanced tree. We show that the worst case complexity of the force evaluation algorithm using a k-d tree is /spl Theta/(nlog/su... View full abstract»

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