30th Annual Symposium on Foundations of Computer Science

30 Oct.-1 Nov. 1989

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  • 30th Annual Symposium on Foundations of Computer Science (Cat. No.89CH2808-4)

    Publication Year: 1989
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    Freely Available from IEEE
  • Simulating (log/sup c/n)-wise independence in NC

    Publication Year: 1989, Page(s):2 - 7
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (533 KB)

    A general framework is developed for removing randomness from randomized NC algorithms whose analysis uses only polylogarithmic independence. Previously, no techniques were known to determinize those RNC algorithms depending on more than constant independence. One application of the techniques is an NC algorithm for the set discrepancy problem, which can be used to obtain many other NC algorithms,... View full abstract»

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  • The probabilistic method yields deterministic parallel algorithms

    Publication Year: 1989, Page(s):8 - 13
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (516 KB)

    A method is provided for converting randomized parallel algorithms into deterministic parallel algorithms. The approach is based on a parallel implementation of the method of conditional probabilities. Results obtained by applying the method to the set balancing problem, lattice approximation, edge-coloring graphs, random sampling, and combinatorial constructions are presented. The general form in... View full abstract»

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  • Dispersers, deterministic amplification, and weak random sources

    Publication Year: 1989, Page(s):14 - 19
    Cited by:  Papers (38)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (401 KB)

    The use of highly expanding bipartite multigraphs (called dispersers) to reduce greatly the error of probabilistic algorithms at the cost of few additional random bits is treated. Explicit constructions of such graphs are generalized and used to obtain the following results: (1) The error probability of any RP (BPP) algorithm can be made exponentially small at the cost of only a constant factor in... View full abstract»

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  • On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications

    Publication Year: 1989, Page(s):20 - 25
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (435 KB)

    A mechanism is provided for constructing log-n-wise-independent hash functions that can be evaluated in O(1) time. A probabilistic argument shows that for fixed epsilon <1, a table of n/sup epsilon / random words can be accessed by a small O(1)-time program to compute one important family of hash functions. An explicit algorithm for such a family, which achieves comparable performance for all p... View full abstract»

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  • The strength of weak learnability

    Publication Year: 1989, Page(s):28 - 33
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (514 KB)

    The problem of improving the accuracy of a hypothesis output by a learning algorithm in the distribution-free learning model is considered. A concept class is learnable (or strongly learnable) if, given access to a source of examples from the unknown concept, the learner with high probability is able to output a hypothesis that is correct on all but an arbitrarily small fraction of the instances. ... View full abstract»

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  • A theory of learning simple concepts under simple distributions and average case complexity for the universal distribution

    Publication Year: 1989, Page(s):34 - 39
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (619 KB)

    It is pointed out that in L.G. Valiant's learning model (Commun. ACM, vol.27, p.1134-42, 1984) many concepts turn out to be too hard to learn, whereas in practice, almost nothing we care to learn appears to be not learnable. To model the intuitive notion of learning more closely, it is assumed that learning happens under an arbitrary distribution, rather than under an arbitrary simple distribution... View full abstract»

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  • Generalizing the PAC model: sample size bounds from metric dimension-based uniform convergence results

    Publication Year: 1989, Page(s):40 - 45
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (521 KB)

    The probably approximately correct (PAC) model of learning from examples is generalized. The problem of learning functions from a set X into a set Y is considered, assuming only that the examples are generated by independent draws according to an unknown probability measure on X*Y. The learner's goal is to find a function in a given hypothesis space of functions from X into Y that on average give ... View full abstract»

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  • Learning binary relations and total orders

    Publication Year: 1989, Page(s):46 - 51
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    The problem of designing polynomial prediction algorithms for learning binary relations is studied for an online model in which the instances are drawn by the learner, by a helpful teacher, by an adversary, or according to a probability distribution on the instance space. The relation is represented as an n*m binary matrix, and results are presented when the matrix is restricted to have at most k ... View full abstract»

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  • Efficient NC algorithms for set cover with applications to learning and geometry

    Publication Year: 1989, Page(s):54 - 59
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (590 KB)

    NC approximation algorithms are given for the unweighted and weighted set cover problems. The algorithms use a linear number of processors and give a cover that has at most log n times the optimal size/weight, thus matching the performance of the best sequential algorithms. The set cover algorithm is applied to learning theory, providing an NC algorithm for learning the concept class obtained by t... View full abstract»

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  • Fast matching algorithms for points on a polygon

    Publication Year: 1989, Page(s):60 - 65
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (508 KB)

    The complete graph induced by a set of 2n points on the boundary of a polygon is considered. The edges are assigned weights equal to the Euclidean distance between their endpoints if the endpoints see each other in the polygon, and + infinity otherwise. An O(n log n)-time algorithm is obtained for finding a minimum-weight perfect matching in this graph if the polygon is convex, and an O(n log/sup ... View full abstract»

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  • Ensemble motion planning in trees

    Publication Year: 1989, Page(s):66 - 71
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (467 KB)

    The problem of transporting a set of objects between the vertices of a tree by a unit capacity vehicle that travels along the edges of the tree is considered. For the case in which any object can be dropped at intermediate vertices along its route and picked up later, the authors present algorithms for finding a minimum cost transportation that run in O(k+qn) time and in O(k+n log n) time, where n... View full abstract»

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  • An upper bound on the number of planar k-sets

    Publication Year: 1989, Page(s):72 - 79
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (446 KB)

    Given a set S of n points, a subset X of size k is called a k-set if there is a hyperplane II that separates X from X/sup c/. It is proved that O(n square root k/log/sub */k) is an upper bound for the number of k-sets in the plane, thus improving the previous bound of P. Erdos et al. (A Survey of Combinatorial Theory, North-Holland, 1983, p.139-49) by a factor of log/sub */k. The method can be ext... View full abstract»

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  • The inverse of an automorphism in polynomial time

    Publication Year: 1989, Page(s):82 - 87
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (400 KB)

    The first known polynomial-time algorithm for computing the inverse of a K-algebra automorphism is presented. The algorithm works over a commutative ring K and is based on a polynomial decomposition algorithm. A polynomial-time algorithm for computing the left composition factor of a multivariate decomposition is also presented. Two related open problems are stated.<<ETX>> View full abstract»

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  • Testing permutation polynomials

    Publication Year: 1989, Page(s):88 - 92
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (311 KB)

    The simple test for determining whether an arbitrary polynomial is a permutation polynomial, by producing its list of values, is considered, and it is found that off-the-shelf techniques from computer algebra improve the running time slightly, without requiring any new insights into the problem. A probabilistic variant of the Hermite test that reduces its running time is given. A criterion for per... View full abstract»

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  • Computing irreducible representations of finite groups

    Publication Year: 1989, Page(s):93 - 98
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (477 KB)

    The bit complexity of computing irreducible representations of finite groups is considered. Exact computations in algebraic number fields are performed symbolically. A polynomial-time algorithm for finding a complete set of inequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table is presented. It follows that some representative... View full abstract»

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  • Galois groups and factoring polynomials over finite fields

    Publication Year: 1989, Page(s):99 - 104
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (463 KB)

    Let p be a prime and F be a polynomial with integer coefficients. Suppose that the discriminant of F is not divisible by p, and denote by m the degree of the splitting field of F over Q and by L the maximal size of the coefficients of F. Then, assuming the generalized Riemann hypothesis (GRH), it is shown that the irreducible factors of F modulo p can be found in deterministic time polynomial in d... View full abstract»

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  • Efficient algorithms for independent assignment on graphic and linear matroids

    Publication Year: 1989, Page(s):106 - 111
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (533 KB)

    Efficient algorithms are presented for the matroid intersection problem and generalizations. The algorithm for weighted intersection works by scaling the weights. The cardinality algorithm is a special case that takes advantage of greater structure. Efficiency of the algorithms is illustrated by several implementations. On graphic matroids the algorithms run close to the best bounds for trivial ma... View full abstract»

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  • Flow in planar graphs with multiple sources and sinks

    Publication Year: 1989, Page(s):112 - 117
    Cited by:  Papers (7)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (498 KB)

    Given a planar network with many sources and sinks, the problem of computing the maximum flow from the sources to the sinks is investigated. An algorithm that runs in O(log/sup 2/n) time using O(n/sup 1.5/) processors on an exclusive-read-exclusive-write parallel random-access machine (EREW PRAM) is obtained, when the amount of flow (demand) at each source and sink is assumed as input. When the de... View full abstract»

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  • A randomized maximum-flow algorithm

    Publication Year: 1989, Page(s):118 - 123
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (483 KB)

    The authors present a randomized maximum-flow algorithm, called the PLED (prudent linking excess diminishing) algorithm, whose expected running time is O(nm+n/sup 2/(log n)/sup 3/); this is O(nm) for all except relatively sparse networks. The algorithm is always correct, and in the worst case, which occurs with negligible probability, it take O(nm log n) time. The approach taken is to maintain a p... View full abstract»

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  • Graph products and chromatic numbers

    Publication Year: 1989, Page(s):124 - 128
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (343 KB)

    The problem of computing the chromatic number of a graph is considered. No known approximation algorithm can guarantee a better than O(n/sup 0.4/) coloring on a three-chromatic graph with n vertices. Evidence is provided that it is inherently impossible to achieve a better than n/sup epsilon / ratio in polynomial time by showing that 'breaking the n/sup epsilon / barrier' will automatically lead t... View full abstract»

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  • Lower bounds for the stable marriage problem and its variants

    Publication Year: 1989, Page(s):129 - 133
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (325 KB)

    An instance of the stable marriage problem of size n involves n men and n women. Each participant ranks all members of the opposite sex in order of preference. A stable marriage is a complete matching M=((m/sub 1/, w/sub i1/), (m/sub 2/, w/sub i2/), . . ., (m/sub n/, w/sub in/)) such that no unmatched man and woman prefer each other to their partners in M. A pair (m/sub i/, w/sub j/) is stable if ... View full abstract»

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  • Approximation schemes for constrained scheduling problems

    Publication Year: 1989, Page(s):134 - 139
    Cited by:  Papers (30)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (549 KB)

    Several constrained scheduling problems are considered. The first polynomial approximation schemes for the problem of minimizing maximum completion time in a two-machine flow shop with release dates and for the problem of minimizing maximum lateness for the single and parallel-machine problem with release dates are described. All of these algorithms are based upon the notion of an outline, a set o... View full abstract»

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  • Datalog vs. first-order logic

    Publication Year: 1989, Page(s):142 - 147
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (382 KB)

    The relation between the expressive power of datalog and that of first-order languages, is clarified. It is then proved that every first-order expressible datalog query is bounded. A form of compactness theorem for finite structure implied by this result is examined, and counterexamples to natural generalizations of the above result are given.<<ETX>> View full abstract»

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  • Decidability and expressiveness for first-order logics of probability

    Publication Year: 1989, Page(s):148 - 153
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (493 KB)

    Decidability and expressiveness issues for two first-order logics of probability are considered. In one the probability is on possible worlds, whereas in the other it is on the domain. It turns out that in both cases it takes very little to make reasoning about probability highly undecidable. It is shown that, when the probability is on the domain, if the language contains only unary predicates, t... View full abstract»

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