Topic

# Las Vegas algorithm

About: Las Vegas algorithm is a(n) research topic. Over the lifetime, 130 publication(s) have been published within this topic receiving 4340 citation(s).

##### Papers

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Bell Labs

^{1}06 Jan 1988-

TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.

Abstract: Random sampling is used for several new geometric algorithms. The algorithms are “Las Vegas,” and their expected bounds are with respect to the random behavior of the algorithms. One algorithm reports all the intersecting pairs of a set of line segments in the plane, and requires O(A + n log n) expected time, where A is the size of the answer, the number of intersecting pairs reported. The algorithm requires O(n) space in the worst case. Another algorithm computes the convex hull of a point set in E3 in O(n log A) expected time, where n is the number of points and A is the number of points on the surface of the hull. A simple Las Vegas algorithm triangulates simple polygons in O(n log log n) expected time. Algorithms for half-space range reporting are also given. In addition, this paper gives asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets.

1,138 citations

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07 Jun 1993-

TL;DR: The authors describe a simple universal strategy S/sup univ/, with the property that, for any algorithm A, T(A,S/Sup univ/)=O (l/sub A/log(l/ sub A/)), which is the best performance that can be achieved, up to a constant factor, by any universal strategy.

Abstract: Let A be a Las Vegas algorithm, i.e., A is a randomized algorithm that always produces the correct answer when its stops but whose running time is a random variable. The authors consider the problem of minimizing the expected time required to obtain an answer from A using strategies which simulate A as follows: run A for a fixed amount of time t/sub 1/, then run A independent for a fixed amount of time t/sub 2/, etc. The simulation stops if A completes its execution during any of the runs. Let S=(t/sub 1/, t/sub 2/,. . .) be a strategy, and let l/sub A/=inf/sub S/T(A,S), where T(A,S) is the expected value of the running time of the simulation of A under strategy S. The authors describe a simple universal strategy S/sup univ/, with the property that, for any algorithm A, T(A,S/sup univ/)=O(l/sub A/log(l/sub A/)). Furthermore, they show that this is the best performance that can be achieved, up to a constant factor, by any universal strategy. >

420 citations

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TL;DR: A simple universal strategy scL univ, with the property that, for any algorithm A, T ( A, scLUniv ) = O( lin A log( linA )), is described, which is the best performance that can be achieved, up to a constant factor, by any universal strategy.

Abstract: Let A be a Las Vegas algorithm, i.e., A is a randomized algorithm that always produces the correct answer when it stops but whose running time is a random variable. We consider the problem of minimizing the expected time required to obtain an answer from A using strategies which simulate A as follows: run A for a fixed amount of time t 1 , then run A independently for a fixed amount of time t 2 , etc. The simulation stops if A completes its execution during any of the runs. Let scL = ( t 1 , t 2 ,…) be a strategy, and let l A = inf scL T ( A , scL ), where T ( A , scL ) i s the expected value of the running time of the simulation of A under strategy scL . We describe a simple universal strategy scL univ , with the property that, for any algorithm A , T ( A , scL univ ) = O( lin A log( linA )). Furthermore, we show that this is the best performance that can be achieved, up to a constant factor, by any universal strategy.

247 citations

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01 Apr 1982-

TL;DR: Two parallel algorithms to compute the determinant and characteristic polynomial of n×n-matrices and the gcd of polynomials of degree ≤n and a fast parallel Las Vegas algorithm for the rank of matrices are presented.

Abstract: We present parallel algorithms to compute the determinant and characteristic polynomial of n×n-matrices and the gcd of polynomials of degree ≤n. The algorithms use parallel time O(log2n) and a polynomial number of processors. We also give a fast parallel Las Vegas algorithm for the rank of matrices. All algorithms work over arbitrary fields.

224 citations

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05 May 1982-

TL;DR: Two polynomial time algorithms are described which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity, if X and Y are graphs of eigenvalue multiplicity m.

Abstract: We investigate the connection between the spectrum of a graph, i.e. the eigenvalues of the adjacency matrix, and the complexity of testing isomorphism. In particular we describe two polynomial time algorithms which test isomorphism of undirected graphs whose eigenvalues have bounded multiplicity. If X and Y are graphs of eigenvalue multiplicity m, then the isomorphism of X and Y can be tested by an O(n4m+c) deterministic and by an O(n2m+c) Las Vegas algorithm, where n is the number of vertices of X and Y.

184 citations