Results 1 - 10 of 49

A subexponential lower bound for the Random Facet algorithm for Parity Games

by Oliver Friedmann, Thomas Dueholm Hansen, Uri Zwick
"... Parity Games form an intriguing family of infinite duration games whose solution is equivalent to the solution of important problems in automatic verification and automata theory. They also form a very natural subclass of Deterministic Mean Payoff Games, which in turn is a very natural subclass of t ..."
Abstract - Cited by 6 (5 self) - Add to MetaCart
Matouˇsek, Sharir and Welzl as the Random Facet algorithm. The expected running time of these algorithmsis subexponential in the size of the game, i.e., 2

Errata for: A subexponential lower bound for the Random Facet algorithm for Parity Games

by Oliver Friedmann, Thomas Dueholm, Hansen Uri Zwick , 2014
"... In [Friedmann, Hansen, and Zwick (2011)] and we claimed that the expected number of pivoting steps performed by the Random-Facet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by Random-Facet∗, a variant of Random-Facet that bases i ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
In [Friedmann, Hansen, and Zwick (2011)] and we claimed that the expected number of pivoting steps performed by the Random-Facet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by Random-Facet∗, a variant of Random-Facet that bases

An improved version of the Random-Facet pivoting rule for the simplex algorithm

by Thomas Dueholm Hansen, Uri Zwick , 2015
"... The Random-Facet pivoting rule of Kalai and of Matoušek, Sharir and Welzl is an elegant randomized pivoting rule for the simplex algorithm, the classical combinatorial algorithm for solving linear programs (LPs). The expected number of pivoting steps performed by the simplex algorithm when using th ..."
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The Random-Facet pivoting rule of Kalai and of Matoušek, Sharir and Welzl is an elegant randomized pivoting rule for the simplex algorithm, the classical combinatorial algorithm for solving linear programs (LPs). The expected number of pivoting steps performed by the simplex algorithm when using

The Quickhull algorithm for convex hulls

by C. Bradford Barber, David P. Dobkin, Hannu Huhdanpaa - ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE , 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algo ..."
Abstract - Cited by 713 (0 self) - Add to MetaCart
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental

The random facet simplex algorithm on combinatorial cubes

by Bernd Gärtner - Random Structures & Algorithms , 2001
"... ..."
Abstract - Cited by 14 (1 self) - Add to MetaCart
Abstract not found

A Subexponential Bound for Linear Programming

by Jiri Matousek, Micha Sharir, Emo Welzl - ALGORITHMICA , 1996
"... We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected min{O(d 2 2 d n),e 2 d ln(n / d)+O ( d+ln n)} time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise, the algorith ..."
Abstract - Cited by 185 (15 self) - Add to MetaCart
We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected min{O(d 2 2 d n),e 2 d ln(n / d)+O ( d+ln n)} time in the unit cost model (where we count the number of arithmetic operations on the numbers in the input); to be precise

The Simplex Algorithm in Dimension Three

by Volker Kaibel, Rafael Mechtel, Micha Sharir , Günter M. Ziegler , 2004
"... We investigate the worst-case behavior of the simplex algorithm on linear programs with three variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the “random edge” rule yields the best asymptotic behavior as well as the most complicated analysis. All other ..."
Abstract - Cited by 6 (2 self) - Add to MetaCart
rules turn out to be much easier to study, but also produce worse results: Most of them show essentially worst-possible behavior; this includes both Kalai’s “random-facet” rule, which without dimension restriction is known to be subexponential, as well as Zadeh’s deterministic history-dependent rule

Combinatorial linear programming: Geometry can help

by Bernd Gärtner - Proc. 2nd Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM), Lecture Notes in Computer Science 1518 , 1998
"... We consider a class A of generalized linear programs on the d-cube (due to Matousek) and prove that Kalai's subexponential simplex algorithm Random-Facet is polynomial on all actual linear programs in the class. In contrast, the subexponential analysis is known to be best possible for general ..."
Abstract - Cited by 10 (2 self) - Add to MetaCart
We consider a class A of generalized linear programs on the d-cube (due to Matousek) and prove that Kalai's subexponential simplex algorithm Random-Facet is polynomial on all actual linear programs in the class. In contrast, the subexponential analysis is known to be best possible

THE RANDOM EDGE SIMPLEX ALGORITHM ON DUAL CYCLIC 4-POLYTOPES

by Rafael Gillmann , 2006
"... The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show a ..."
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The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show

A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem

by Gilbert Laporte, Jorge Riera-ledesma, Juan-José Salazar-González - Networks , 1998
"... The purpose of this article is to present a branch-and-cut algorithm for the undirected Traveling Purchaser Problem which consists of determining a minimum-cost route through a subset of markets, where the cost is the sum of travel and purchase costs. The problem is formulated as an integer linear p ..."
Abstract - Cited by 11 (4 self) - Add to MetaCart
of randomly generated instances. Results show that the proposed algorithm outperform all previous approaches and can solve optimally instances containing up to 200 markets.
Results 1 - 10 of 49