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Las Vegas algorithm
About: Las Vegas algorithm is a research topic. Over the lifetime, 130 publications have been published within this topic receiving 4340 citations.
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TL;DR: An adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(mlogn) queries, which is tight up to a constant factor for classes of non-dense graphs, and a lower bound of @W((2m/r)^r^/^2) for learning the class ofNon-uniform hypergraphs of dimension r with m edges.
59 citations
TL;DR: The main goal of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation for the complexity measures of one-way communication, ordered binary decision diagrams, and finite automata.
Abstract: The study of the computational power of randomized computations is one of the central tasks of complexity theory. The main goal of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation. We investigate the power of Las Vegas computation for the complexity measures of one-way communication, ordered binary decision diagrams, and finite automata. (i) For the one-way communication complexity of two-party protocols we show that Las Vegas communication can save at most one half of the deterministic one-way communication complexity. We also present a language for which this gap is tight. (ii) The result (i) is applied to show an at most polynomial gap between determinism and Las Vegas for ordered binary decision diagrams. (iii) For the size (i.e., the number of states) of finite automata we show that the size of Las Vegas finite automata recognizing a language L is at least the square root of the size of the minimal deterministic finite automaton recognizing L. Using a specific language we verify the optimality of this bound. Copyright 2001 Academic Press.
58 citations
TL;DR: In this paper, a 2-player random game with supports of size two with high probability has been shown to have a Nash equilibrium with support complexity at least 1 - O(1/log n).
Abstract: We consider Nash equilibria in 2-player random games and analyze a simple Las Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a Nash equilibrium; on m × n payoff matrices, it runs in time O(m2nloglog n + n2mloglog m) with high probability. Our result follows from showing that a 2-player random game has a Nash equilibrium with supports of size two with high probability, at least 1 - O(1/log n). Our main tool is a polytope formulation of equilibria. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007
58 citations
TL;DR: A randomized algorithm that triangulates a simple polygon onn vertices inO(n log*n) expected time is presented; the bound holds for any input polygon.
Abstract: We present a randomized algorithm that triangulates a simple polygon onn vertices inO(n log*n) expected time. The averaging in the analysis of running time is over the possible choices made by the algorithm; the bound holds for any input polygon.
58 citations
01 Jul 2004
TL;DR: An adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(m log n) queries, which is tight up to a constant factor for classes of non-dense graphs, and a non-adaptive Monte Carlo algorithm that succeeds with probability at least 1–n − − c.
Abstract: We consider the problem of learning a general graph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden graph. This model has been studied for particular classes of graphs by Kucherov and Grebinski [1] and Alon et al.[2], motivated by problems arising in genome sequencing. We give an adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(m log n) queries, which is tight up to a constant factor for classes of non-dense graphs. Allowing randomness, we give a 5-round Las Vegas algorithm using \(O(m {\rm log}n+\sqrt{m}{\rm log}^{2}n)\) queries in expectation. We give a lower bound of Ω((2m/r) r/2) for learning the class of non-uniform hypergraphs of dimension r with m edges. For the class of r-uniform hypergraphs with bounded degree d, where d≤ n 1/( r− − 1)/(2r 1 + 2/( r− − 1)), we give a non-adaptive Monte Carlo algorithm using O(dnlog n) queries, which succeeds with probability at least 1–n − − c, where c is any constant.
55 citations