The Experts below are selected from a list of 103872 Experts worldwide ranked by ideXlab platform

Corey Proscia - One of the best experts on this subject based on the ideXlab platform.

Steve Mahaney - One of the best experts on this subject based on the ideXlab platform.

  • A quasi-Polynomial-Time Algorithm for sampling words from a context-free language
    Information and Computation, 1997
    Co-Authors: Vivek Gore, Mark Jerrum, Sampath Kannan, Z. Sweedyk, Steve Mahaney
    Abstract:

    Abstract A quasi-Polynomial-Time Algorithm is presented for sampling almost uniformly at random from then-slice of the languageL(G) generated by an arbitrary context-free grammarG. (Then-slice of a languageLover an alphabetΣis the subsetL∩Σnof words of length exactlyn.) The Time complexity of the Algorithm ise−2(n |G|)O(log n)where the parameterebounds the variation of the output distribution from uniform, and |G| is a natural measure of the size of grammarG. The Algorithm applies to a class of language sampling problems that includes slices of context-free languages as a proper subclass. For the restricted case of homogeneous languages expressed by regular expressions without Kleene-star, a truly Polynomial-Time Algorithm is presented.

Michael Saks - One of the best experts on this subject based on the ideXlab platform.

  • A Polynomial Time Algorithm for Lossy Population Recovery
    arXiv: Data Structures and Algorithms, 2013
    Co-Authors: Ankur Moitra, Michael Saks
    Abstract:

    We give a Polynomial Time Algorithm for the lossy population recovery problem. In this problem, the goal is to approximately learn an unknown distribution on binary strings of length $n$ from lossy samples: for some parameter $\mu$ each coordinate of the sample is preserved with probability $\mu$ and otherwise is replaced by a `?'. The running Time and number of samples needed for our Algorithm is Polynomial in $n$ and $1/\varepsilon$ for each fixed $\mu>0$. This improves on Algorithm of Wigderson and Yehudayoff that runs in quasi-Polynomial Time for any $\mu > 0$ and the Polynomial Time Algorithm of Dvir et al which was shown to work for $\mu \gtrapprox 0.30$ by Batman et al. In fact, our Algorithm also works in the more general framework of Batman et al. in which there is no a priori bound on the size of the support of the distribution. The Algorithm we analyze is implicit in previous work; our main contribution is to analyze the Algorithm by showing (via linear programming duality and connections to complex analysis) that a certain matrix associated with the problem has a robust local inverse even though its condition number is exponentially small. A corollary of our result is the first Polynomial Time Algorithm for learning DNFs in the restriction access model of Dvir et al.

  • FOCS - A Polynomial Time Algorithm for Lossy Population Recovery
    2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013
    Co-Authors: Ankur Moitra, Michael Saks
    Abstract:

    We give a Polynomial Time Algorithm for the lossy population recovery problem. In this problem, the goal is to approximately learn an unknown distribution on binary strings of length n from lossy samples: for some parameter m each coordinate of the sample is preserved with probability m and otherwise is replaced by a `?'. The running Time and number of samples needed for our Algorithm is Polynomial in n and 1/e for each fixed m>0. This improves on Algorithm of Wigderson and Yehudayoff that runs in quasi-Polynomial Time for any m > 0 and the Polynomial Time Algorithm of Dvir et al which was shown to work for m > rapprox 0.30 by Batman et al. In fact, our Algorithm also works in the more general framework of Batman et al. in which there is no a priori bound on the size of the support of the distribution. The Algorithm we analyze is implicit in previous work; our main contribution is to analyze the Algorithm by showing (via linear programming duality and connections to complex analysis) that a certain matrix associated with the problem has a robust local inverse even though its condition number is exponentially small. A corollary of our result is the first Polynomial Time Algorithm for learning DNFs in the restriction access model of Dvir et al [9].

Shigeru Masuyama - One of the best experts on this subject based on the ideXlab platform.

  • A Polynomial Time Algorithm for obtaining minimum edge ranking on two-connected outerplanar graphs
    Information Processing Letters, 2007
    Co-Authors: Shin-ichi Nakayama, Shigeru Masuyama
    Abstract:

    An edge ranking of a graph G is a labeling r of its edges with positive integers such that every path between two different edges e"u, e"v with the same rank r(e"u)=r(e"v) contains an intermediate edge e"w with rank r(e"w)>r(e"u). An edge ranking of G is minimum if the largest rank k assigned is the smallest among all rankings of G. The edge ranking problem is to find a minimum edge ranking of given graph G. This problem is NP-hard and no Polynomial Time Algorithm for solving it is known for non-trivial classes of graphs other than the class of trees. In this paper, we first show, on a general graph G, a relation between a minimum edge ranking of G and its minimal cuts, which ensures that we can obtain a Polynomial Time Algorithm for obtaining minimum edge ranking of a given graph G if minimal cuts for each subgraph of G can be found in Polynomial Time and the number of those is Polynomial. Based on this relation, we develop a Polynomial Time Algorithm for finding a minimum edge ranking on a 2-connected outerplanar graph.

  • A Polynomial Time Algorithm for Obtaining a Minimum Vertex Ranking Spanning Tree in Outerplanar Graphs
    IEICE Transactions on Information and Systems, 2006
    Co-Authors: Shin-ichi Nakayama, Shigeru Masuyama
    Abstract:

    The minimum vertex ranking spanning tree problem is to find a spanning tree of G whose vertex ranking is minimum. This problem is NP-hard and no Polynomial Time Algorithm for solving it is known for non-trivial classes of graphs other than the class of interval graphs. This paper proposes a Polynomial Time Algorithm for solving the minimum vertex ranking spanning tree problem on outerplanar graphs.

Christopher Clingerman - One of the best experts on this subject based on the ideXlab platform.