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• W2037741686 abstract "Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type 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 proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection)." @default.
• W2037741686 created "2016-06-24" @default.
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• W2037741686 date "2008-06-01" @default.
• W2037741686 modified "2023-09-23" @default.
• W2037741686 title "Violator spaces: Structure and algorithms" @default.
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• W2037741686 doi "https://doi.org/10.1016/j.dam.2007.08.048" @default.
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