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32
The Domination Heuristic for LPtype Problems
, 2009
"... Certain geometric optimization problems, for example finding the smallest enclosing ellipse of a set of points, can be solved in linear time by simple randomized (or complicated deterministic) combinatorial algorithms. In practice, these algorithms are enhanced or replaced with heuristic variants th ..."
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known abstract class of LPtype problems; its effectiveness in practice depends on whether and how fast the heuristic can be implemented for the specific problem at hand, and on whether the input distribution is favorable. We provide test results showing that for two concrete problems, the new heuristic may lead
Three views of LPtype optimization problems
, 2003
"... An axiomatically defined class of optimization problems, called LPtype problems (or also generalized linear programming problems) and introduced by Sharir and Welzl, includes linear programming, the smallest enclosing ball for a given point set in R , and many other important problems. We inv ..."
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An axiomatically defined class of optimization problems, called LPtype problems (or also generalized linear programming problems) and introduced by Sharir and Welzl, includes linear programming, the smallest enclosing ball for a given point set in R , and many other important problems. We
Removing degeneracy in LPtype problems revisited
"... LPtype problems is a successful axiomatic framework for optimization problems capturing, e.g., linear programming and the smallest enclosing ball of a point set. In [Matouˇsek and ˇ Skovroň, Theory of Computing 3(2007) 159–177] it was proved that in order to remove degeneracies of an LPtype proble ..."
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Cited by 2 (0 self)
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LPtype problems is a successful axiomatic framework for optimization problems capturing, e.g., linear programming and the smallest enclosing ball of a point set. In [Matouˇsek and ˇ Skovroň, Theory of Computing 3(2007) 159–177] it was proved that in order to remove degeneracies of an LPtype
Removing Degeneracies in LPtype Problems May Need to Increase Dimension
, 2006
"... LPtype problems are an abstract model of linear programming. For some applications it is useful to have LPtype problems satisfying a special property: nondegeneracy. For any LPtype problem there is a nondegenerate refinement, however the complexity measured by the combinatorial dimension may nee ..."
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LPtype problems are an abstract model of linear programming. For some applications it is useful to have LPtype problems satisfying a special property: nondegeneracy. For any LPtype problem there is a nondegenerate refinement, however the complexity measured by the combinatorial dimension may
Discrete and lexicographic Helly theorems and their relations to LPtype problems
 IN PROC. 45TH IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS
, 2004
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Journal of Computational Geometry jocg.org SAMPLING WITH REMOVAL IN LPTYPE PROBLEMS∗
"... Abstract. Random sampling is an important tool in optimization subject to finitely or infinitely many constraints. Here we are interested in obtaining solutions of low cost that violate only few constraints. Under convexity or similar favorable conditions, and assuming fixed dimension, one can indee ..."
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the question in the completely combinatorial setting of LPtype problems, which allows a unified treatment of many different optimization problems. Given a nondegenerate LPtype problem of combinatorial dimension δ, we consider sampling with subsequent removal of the k constraints that lead to the best
Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All Lptype Problems
, 2007
"... We show that a Simple Stochastic Game (SSG) can be formulated as an LPtype problem. Using this formulation, and the known algorithm of Sharir and Welzl [SW] for LPtype problems, we obtain the first strongly subexponential solution for SSGs (a strongly subexponential algorithm has only been known ..."
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Cited by 23 (0 self)
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We show that a Simple Stochastic Game (SSG) can be formulated as an LPtype problem. Using this formulation, and the known algorithm of Sharir and Welzl [SW] for LPtype problems, we obtain the first strongly subexponential solution for SSGs (a strongly subexponential algorithm has only been known
Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 114 (10 self)
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programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement
Testing Roundness of a Polytope and Related Problems (Extended Abstract)
"... In this paper we study the problem of computing the smallestwidth annulus for a convex polytope in R d . This generalizes a topic from tolerancing metrology to higher dimensions, of which the planar case has been investigated by Swanson, Lee and Wu. We show this problem to be equivalent to the pr ..."
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to the problem of computing different variants of Hausdorffminimal spheres. We can formulate the latter problem as a LPtype problem with combinatorial dimension 2(d + 1) (for the planar case: 4) and prove the uniqueness of Hausdorffminimal spheres for arbitrary convex bodies. The result is an expected linear
Violator Spaces: Structure and Algorithms
, 2007
"... Sharir and Welzl introduced an abstract framework for optimization problems, called LPtype problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a p ..."
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Cited by 8 (2 self)
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Sharir and Welzl introduced an abstract framework for optimization problems, called LPtype problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a
Results 1  10
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32