Showing papers on "Las Vegas algorithm published in 2008"
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 proof introduces an associative *-ring as a tool for studying central products of p-groups and leads to a translation of the problem into classical linear algebra which can be solved by application of the MeatAxe and other established module-theoretic algorithms.
Abstract: Polynomial-time algorithms are given to find a central decomposition of maximum size for a finite p-group of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of finite *-rings and also the Las Vegas C-MeatAxe. When p is small, the probabilistic methods can be replaced by deterministic polynomial-time algorithms.
The methods introduce new group isomorphism invariants including new characteristic subgroups.
25 citations
17 May 2008
TL;DR: In the difficult case of the discriminant Δ of a certain quadratic order being positive, a Las Vegas algorithm is developed for solving the principal ideal problem that executes in expected time bounded by O(Δ1/6+Ɛ), whereas the complexity of Lagrange's (unconditional) techniquefor solving this problem is O( Δ1/2-Ɛ).
Abstract: The general binary quadratic Diophantine equationax2 + bxy + cy2 + dx + ey + f = 0was first solved by Lagrange over 200 years ago Since that time littleimprovement has been made to Lagrange's technique In this paper weshow how to reduce this problem to that of determining whether or notan ideal of a certain quadratic order is principal and if so exhibitinga generator of that ideal In the difficult case of the discriminant Δ ofthis order being positive, we develop a Las Vegas algorithm for solvingthe principal ideal problem that executes in expected time bounded byO(Δ1/6+Ɛ), whereas the complexity of Lagrange's (unconditional) techniquefor solving this problem is O(Δ1/2+Ɛ)
7 citations
01 Oct 2008
TL;DR: This chapter presents a new single shot random algorithm named RSRT for Rapidly-exploring Sorted Random Tree, an improvement of previous probabilistic motion planning algorithms to address problems that involve wide configuration spaces and experiments show practical performances of each improvement.
Abstract: Las Vegas algorithm is a powerful paradigm for a class of decision problems that has at least a theoretical exponential resolving time Motion planning problems are one of those and are out to be solved only by high computational systems due to such a complexity (Schwartz & Sharir, 1983) As Las Vegas algorithms have a randomized way to meet problem solutions (Latombe 1991), the complexity is reduced to polynomial runtime In this chapter, we present a new single shot random algorithm for motion planning problems This algorithm named RSRT for Rapidly-exploring Sorted Random Tree is based on inherent relation analysis between Rapidly-exploring Random Tree components, named RRT components (LaValle, 2004) RRT is an improvement of previous probabilistic motion planning algorithms to address problems that involve wide configuration spaces As the main goal of the discipline is to develop practical and efficient solvers that automatically produce motion, RRT methods successfully reduce the complexity in exploring the space partially and producing non-deterministic solutions close to optimal ones In the classical RRT algorithm, space is explored by repeating successively three phases: generation of a random configuration in the whole space (including free and non-free space); selection of a nearest configuration; and generation of a new configuration obtained by numerical integration over a fixed time step Then the motion planning process is discretized into steps from the initial configuration to other configurations in the space In such a way, RRT algorithms are the motion planners last generation that generally addresses a large set of motion planning problems Mobile, geometrical or functional constraints, input methods and collision detection are unspecified As it is possible to measure solutions provided by RRT, RSRT or other improvements in spaces with arbitrary dimension, experiments are realized on a wide set of path planning problems involving various mobiles in static and dynamic environments We experiment the RSRT and other RRT algorithms using various configurations spaces to produce a massive experiment analysis: from free flying to constraint mobiles, from single to articulated mobiles, from wide to narrow spaces, from simple to complex distance metric evaluations, from special to randomly generated spaces These experiments show practical performances of each improvement, and results reflect their classical behavior on each type of motion planning problems