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49
A subexponential lower bound for the Random Facet algorithm for Parity Games
"... 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 ..."
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Cited by 6 (5 self)
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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
, 2014
"... In [Friedmann, Hansen, and Zwick (2011)] and we claimed that the expected number of pivoting steps performed by the RandomFacet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by RandomFacet∗, a variant of RandomFacet that bases i ..."
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Cited by 2 (2 self)
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In [Friedmann, Hansen, and Zwick (2011)] and we claimed that the expected number of pivoting steps performed by the RandomFacet algorithm of Kalai and of Matoušek, Sharir, and Welzl is equal to the expected number of pivoting steps performed by RandomFacet∗, a variant of RandomFacet that bases
An improved version of the RandomFacet pivoting rule for the simplex algorithm
, 2015
"... The RandomFacet 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 RandomFacet 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
 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 twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 713 (0 self)
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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 twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental
The random facet simplex algorithm on combinatorial cubes
 Random Structures & Algorithms
, 2001
"... ..."
A Subexponential Bound for Linear Programming
 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 ..."
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Cited by 185 (15 self)
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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
, 2004
"... We investigate the worstcase behavior of the simplex algorithm on linear programs with three variables, that is, on 3dimensional 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 ..."
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Cited by 6 (2 self)
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rules turn out to be much easier to study, but also produce worse results: Most of them show essentially worstpossible behavior; this includes both Kalai’s “randomfacet” rule, which without dimension restriction is known to be subexponential, as well as Zadeh’s deterministic historydependent rule
Combinatorial linear programming: Geometry can help
 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 dcube (due to Matousek) and prove that Kalai's subexponential simplex algorithm RandomFacet is polynomial on all actual linear programs in the class. In contrast, the subexponential analysis is known to be best possible for general ..."
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Cited by 10 (2 self)
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We consider a class A of generalized linear programs on the dcube (due to Matousek) and prove that Kalai's subexponential simplex algorithm RandomFacet 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 4POLYTOPES
, 2006
"... The simplex algorithm using the random edge pivotrule on any realization of a dual cyclic 4polytope with n facets does not take more than O(n) pivotsteps. 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 pivotrule on any realization of a dual cyclic 4polytope with n facets does not take more than O(n) pivotsteps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show
A BranchandCut Algorithm for the Undirected Traveling Purchaser Problem
 Networks
, 1998
"... The purpose of this article is to present a branchandcut algorithm for the undirected Traveling Purchaser Problem which consists of determining a minimumcost 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 ..."
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Cited by 11 (4 self)
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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
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49