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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
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    Freely Available from IEEE
  • Approximate strip packing

    Publication Year: 1996, Page(s):31 - 36
    Cited by:  Papers (10)
    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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  • Author index

    Publication Year: 1996
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    Freely Available from IEEE
  • New lower bounds for halfspace emptiness

    Publication Year: 1996, Page(s):472 - 481
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (820 KB)

    The author derives a lower bound of Ω(n4/3) for the halfspace emptiness problem: given a set of n points and n hyperplanes in R5, is every point above every hyperplane? This matches the best known upper bound to within polylogarithmic factors, and improves the previous best lower bound of Ω(nlogn). The lower bound applies to partitioning algorithms in whi... View full abstract»

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  • Computing vertex connectivity: new bounds from old techniques

    Publication Year: 1996, Page(s):462 - 471
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (916 KB)

    The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3+n,κn}m); for an undirected graph the term m can be replace... View full abstract»

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  • Clique is hard to approximate within n1-ϵ

    Publication Year: 1996, Page(s):627 - 636
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (876 KB)

    The author proves that unless NP=coR, Max Clique is hard to approximate in polynomial time within a factor n1-ε for any ε>0. This is done by, for any δ>0, constructing a proof system for NP which uses δ amortized free bits. A central lemma, which might be of independent interest, gives sufficient conditions (in the form of a certain type of agreement) for cre... View full abstract»

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  • All pairs almost shortest paths

    Publication Year: 1996, Page(s):452 - 461
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 KB)

    Let G=(V,E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of D. Aingworth et al. (1996), we describe an O˜(min{n3/2m1/2,n7/3 }) time algorithm APASP2 for computing all distan... 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 (832 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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  • Gadgets, approximation, and linear programming

    Publication Year: 1996, Page(s):617 - 626
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    The authors present a linear-programming based method for finding “gadgets”, i.e., combinatorial structures reducing constraints of one optimization problem to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method they present a number of new, computer-constructed gadgets for several different redu... View full abstract»

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  • Static dictionaries on AC0 RAMs: query time &thetas;(√log n/log log n) is necessary and sufficient

    Publication Year: 1996, Page(s):441 - 450
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (868 KB)

    In this paper we consider solutions to the static dictionary problem on AC0 RAMs, i.e. random access machines where the only restriction on the finite instruction set is that all computational instructions are in AC0. Our main result is a tight upper and lower bound of θ(√log n/log log n) on the time for answering membership queries in a set of size n when reasona... 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 (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (552 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 (... View full abstract»

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  • Verifying identities

    Publication Year: 1996, Page(s):612 - 616
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB)

    The authors provide an O˜(n2) time randomized algorithm to check whether a given operation f:S×S→S is associative (letting n=|S|). They prove this performance is optimal (up to polylogarithmic factors) even in case the operation is “cancellative”. No sub-n3 algorithm was previously known for this task. More generally they give an O(nc )... View full abstract»

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  • Simplified and improved resolution lower bounds

    Publication Year: 1996, Page(s):274 - 282
    Cited by:  Papers (31)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (684 KB)

    We give simple new lower bounds on the lengths of resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds significantly extend the range of formula sizes for which non-trivial lower bounds are known. For example, we show that with probability approaching 1, any resolution refutation of a randomly chosen 3-CNF formula with at most n6/... 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 (800 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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  • Efficient approximate and dynamic matching of patterns using a labeling paradigm

    Publication Year: 1996, Page(s):320 - 328
    Cited by:  Papers (13)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (692 KB)

    A key approach in string processing algorithmics has been the labeling paradigm which is based on assigning labels to some of the substrings of a given string. If these labels are chosen consistently, they can enable fast comparisons of substrings. Until the first optimal parallel algorithm for suffix tree construction was given by the authors in 1994 the labeling paradigm was considered not to be... View full abstract»

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  • Potential of the approximation method

    Publication Year: 1996, Page(s):431 - 440
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (748 KB)

    Developing some techniques for the approximation method, we establish precise versions of the following statements concerning lower bounds for circuits that detect cliques of size s in a graph with m vertices. For 5⩽s⩽m/4, a monotone circuit computing CLIQUE(m, s) contains at least (1/2) 1.8min(√s-12,m/(4s))/ gates. If a non-monotone circuit computes CLIQUE using a “... View full abstract»

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  • Polynomial time approximation schemes for Euclidean TSP and other geometric problems

    Publication Year: 1996, Page(s):2 - 11
    Cited by:  Papers (44)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (908 KB)

    We present a polynomial time approximation scheme for Euclidean TSP in ℜ2. Given any n nodes in the plane and ε>0, the scheme finds a (1+ε)-approximation to the optimum traveling salesman tour in time n0(1/ε). When the nodes are in ℜd, the running time increases to n(O˜(logd-2n)/εd-1) The previous best appr... View full abstract»

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  • Efficient self-testing/self-correction of linear recurrences

    Publication Year: 1996, Page(s):602 - 611
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (900 KB)

    The authors consider the problem of designing self-testers/self-correctors for functions defined by linear recurrences. They present the first complete package of efficient and simple self-testers, self-correctors, and result-checkers for such functions. The results are proved by demonstrating an efficient reduction from this problem to the problem of testing linear functions over certain matrix g... View full abstract»

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  • Equivalence in finite-variable logics is complete for polynomial time

    Publication Year: 1996, Page(s):264 - 273
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (932 KB)

    How difficult is it to decide whether two finite structures can be distinguished in a given logic? For first order logic, this question is equivalent to the graph isomorphism problem with its well-known complexity theoretic difficulties. Somewhat surprisingly, the situation is much clearer when considering the fragments Lk of first-order logic whose formulae contain at most k (free or b... View full abstract»

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  • Universal data compression and portfolio selection

    Publication Year: 1996, Page(s):534 - 538
    Cited by:  Papers (5)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (360 KB)

    The authors consider universal data compression, universal portfolio selection (online portfolio algorithms) and the relationship of both to information theory. Apparently the fundamental minimax redundancy game in data compression and the minimax regret game for the growth rate of wealth in investment have the same answer. There is also a duality between entropy rate and the growth rate of wealth 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 (488 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{[√(logn)][logn/logw+loglogn][logwloglogn]}) time per operation, including insert, delete, member search, and neighbour search. The cost for searching is worst-case while ... View full abstract»

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  • On the knowledge complexity of 𝒩𝒫

    Publication Year: 1996, Page(s):494 - 503
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (868 KB)

    The authors show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class 𝒜ℳ∩co-𝒜ℳ. Thus, if the polynomial time hierarchy does not collapse, then 𝒩𝒫-complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict 𝒩𝒫 languag... View full abstract»

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  • Approximating minimum-size k-connected spanning subgraphs via matching

    Publication Year: 1996, Page(s):292 - 301
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (892 KB)

    An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of a given (undirected or directed) graph G=(V,E). There are four versions of the problem, depending on whether G is undirected or directed, and whether the spanning subgraph is required to be k-node connected (k-NCSS) or k-edge connected (k-ECSS). The approximation guarantees are as follows... 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 (604 KB)

    We present a randomized algorithm which takes as input n distinct points {(xi,yi)}i=1n from F×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., yi=f(xi) for at... View full abstract»

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  • Property testing and its connection to learning and approximation

    Publication Year: 1996, Page(s):339 - 348
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (984 KB)

    The authors study the question of determining whether an unknown function has a particular property or is ε-far from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, they establish some connections between propert... View full abstract»

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