[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science

24-26 Oct. 1988

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  • 29th Annual Symposium on Foundations of Computer Science (IEEE Cat. No.88CH2652-6)

    Publication Year: 1988
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    Freely Available from IEEE
  • Results on learnability and the Vapnik-Chervonenkis dimension

    Publication Year: 1988, Page(s):120 - 129
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (724 KB)

    The problem of learning a concept from examples in a distribution-free model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite Vapnik-Chervonenkis (VC) dimension. An important variation on the probl... View full abstract»

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  • On the complexity of kinodynamic planning

    Publication Year: 1988, Page(s):306 - 316
    Cited by:  Papers (37)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    The following problem, is considered: given a robot system find a minimal-time trajectory from a start position and velocity to a goal position and velocity, while avoiding obstacles and respecting dynamic constraints on velocity and acceleration. The simplified case of a point mass under Newtonian mechanics together with velocity and acceleration bounds is considered. The point must be flown from... View full abstract»

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  • Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators

    Publication Year: 1988, Page(s):296 - 305
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (700 KB)

    Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. It is shown that within this evaluation-box representation, the polynomial greatest common divisor and factorization problems as well as the problem of extracting the numerator and denominator of a rational fun... View full abstract»

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  • A faster PSPACE algorithm for deciding the existential theory of the reals

    Publication Year: 1988, Page(s):291 - 295
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (356 KB)

    The decision problem for the existential theory of the reals is the problem of deciding if the set {x∈Rn ; P(x) is nonempty, where P(x) is a predicate which is a Boolean function of atomic predicates either of which is a Boolean function of atomic predicates either of the form fi(x)⩾0 or f View full abstract»

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  • Lower bounds for integer greatest common divisor computations

    Publication Year: 1988, Page(s):54 - 63
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (656 KB)

    An Ω(log log n) lower bound is proved on the depth of any computation tree with operations {+, -, /, mod, ⩽} that computes the greatest common divisor (GCD) of all pairs of n-bit integers. A novel technique for handling the truncation operation is implicit in the proof. Also proved is a Θ(n) bound on the depth of any algebraic computation trees with opera... View full abstract»

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  • New algorithms for finding irreducible polynomials over finite fields

    Publication Year: 1988, Page(s):283 - 290
    Cited by:  Papers (12)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (556 KB)

    An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministic-polynomial-time reducible to the problem of facto... View full abstract»

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  • Polytopes, permanents and graphs with large factors

    Publication Year: 1988, Page(s):412 - 421
    Cited by:  Papers (8)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB)

    Randomized algorithms for approximating the number of perfect matchings in a graph are considered. An algorithm that is a natural simplification of one suggested and analyzed previously is introduced and analyzed. One of the key ideas is to view the analysis from a geometric perspective: it is proved that for any graph G the k-slice of the well-known Edmonds matching polytope has... View full abstract»

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  • Speeding up dynamic programming

    Publication Year: 1988, Page(s):488 - 496
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (672 KB)

    A number of important computational problems in molecular biology, geology, speech recognition, and other areas can be expressed as recurrences which have typically been solved with dynamic programming. By using more sophisticated data structures, and by taking advantage of further structure from the applications, the authors speed up the computation of several of these recurrences by one or two o... View full abstract»

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  • Achieving oblivious transfer using weakened security assumptions

    Publication Year: 1988, Page(s):42 - 52
    Cited by:  Papers (54)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (816 KB)

    The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophistica... View full abstract»

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  • Genus g graphs have pagenumber O(√g)

    Publication Year: 1988, Page(s):458 - 468
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The following results are presented: (1) any graph of genus g has pagenumber O(√g); and (2) most n-ver... View full abstract»

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  • Efficient parallel algorithms for chordal graphs

    Publication Year: 1988, Page(s):150 - 161
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1012 KB)

    The author gives efficient parallel algorithms for recognizing chordal graphs, finding a maximum clique and a maximum independent set in a chordal graph, finding an optimal coloring of a chordal graph, finding a breadth-first search tree and a depth-first search tree of a chordal graph, recognizing interval graphs, and testing interval graphs for isomorphism. The key to the results is an efficient... View full abstract»

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  • Near-optimal time-space tradeoff for element distinctness

    Publication Year: 1988, Page(s):91 - 97
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (408 KB)

    It was conjectured by A. Borodin et al. that to solve the element distinctness problem requires TS=Ω(n2) on a comparison-based branching program using space S and time T, which, if true, would be close to optimal since TS=O(n2 log n) is achievable. They showed recently (1987) that TS=Ω(n<... View full abstract»

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  • On the existence of pseudorandom generators

    Publication Year: 1988, Page(s):12 - 24
    Cited by:  Papers (10)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (808 KB)

    Pseudorandom generators are known to exist, assuming the existence of functions that cannot be efficiently inverted on the distributions induced by applying the function iteratively polynomially many times. This sufficient condition is also necessary, but it is difficult to check whether particular functions, assumed to be one-way, are also one-way on their iterates. This raises the fundamental qu... View full abstract»

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  • Fast management of permutation groups

    Publication Year: 1988, Page(s):272 - 282
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (968 KB)

    Novel algorithms for computation in permutation groups are presented. They provide an order-of-magnitude improvement in the worst-case analysis of the basic permutation-group problems, including membership testing and computing the order of the group. For deeper questions about the group, including finding composition factors, an improvement of up to four orders of magnitude is realized. These and... View full abstract»

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  • A deterministic view of random sampling and its use in geometry

    Publication Year: 1988, Page(s):539 - 549
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (916 KB)

    A number of efficient probabilistic algorithms based on the combination of divide-and-conquer and random sampling have been recently discovered. It is shown that all those algorithms can be derandomized with only polynomial overhead. In the process. results of independent interest concerning the covering of hypergraphs are established, and various probabilistic bounds in geometry complexity are im... View full abstract»

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  • Constructive results from graph minors: linkless embeddings

    Publication Year: 1988, Page(s):398 - 409
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (844 KB)

    A formal study of three-dimensional topological graph theory is initiated. The problem of deciding whether a graph can be embedded in 3-space so that no collection of vertex-disjoint cycles is topologically linked is considered first. The Robertson-Seymour Theory of Graph Minors is applicable to this problem and guarantees the existence of an O(n 3) algorithm for the decision p... View full abstract»

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  • Combinatorial algorithms for the generalized circulation problem

    Publication Year: 1988, Page(s):432 - 443
    Cited by:  Papers (6)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1028 KB)

    A generalization of the maximum-flow problem is considered in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e)λ(e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exc... View full abstract»

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  • Bounds on the cover time

    Publication Year: 1988, Page(s):479 - 487
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (500 KB)

    A particle that moves on a connected unidirected graph G with n vertices is considered. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph, starting from a given vertex. Upper and lower bounds are presented that relate the expected ... View full abstract»

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  • Homogeneous measures and polynomial time invariants

    Publication Year: 1988, Page(s):36 - 41
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (280 KB)

    The usual probability distributions are concentrated on strings that do not differ noticeably in any fundamental characteristics, except their informational size (Kolmogorov complexity). The formalization of this statement is given and shown to distinguish a class of homogeneous probability measures suggesting various applications. In particular, it could explain why the average case NP-completene... View full abstract»

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  • A Las Vegas algorithm for linear programming when the dimension is small

    Publication Year: 1988, Page(s):452 - 456
    Cited by:  Papers (13)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (320 KB)

    An algorithm for solving linear programming problems is given. The expected number of arithmetic operations required by the algorithm is given. The expectation is with respect to the random choices made by the algorithm, and the bound holds for any given input. The technique can be extended to other convex programming problems View full abstract»

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  • Effect of connectivity in associative memory models

    Publication Year: 1988, Page(s):138 - 147
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (672 KB)

    The authors investigate how good connectivity properties translate into good error-correcting behavior in sparse networks of threshold elements. They determine how the eigenvalues of the interconnection graph (which in turn reflect connectivity properties) relate to the quantities, number of items stored, amount of error-correction, radius of attraction, and rate of convergence in an associative m... View full abstract»

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  • Lattices, mobius functions and communications complexity

    Publication Year: 1988, Page(s):81 - 90
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (788 KB)

    A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory View full abstract»

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  • Hardness vs. randomness

    Publication Year: 1988, Page(s):2 - 11
    Cited by:  Papers (27)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (584 KB)

    A simple construction for a pseudorandom bit generator is presented. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g. P, NC, PSPACE, etc.), using an arbitrary function that is hard for C. This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudora... View full abstract»

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  • Universal packet routing algorithms

    Publication Year: 1988, Page(s):256 - 269
    Cited by:  Papers (29)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1312 KB)

    The packet-routing problem is examined in a network-independent context. The goal is to devise a strategy for routing that works well for a wide variety of networks. To achieve this goal, the routing problem is partitioned into two stages: a path-selection stage and a scheduling stage. In the first stage, paths for the packets are found with small maximum distance and small maximum congestion. Onc... View full abstract»

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