Total Dual Integrality in Some Facility Location Problems
نویسندگان
چکیده
منابع مشابه
Title Total Dual Integrality in Some Facility Location Problems
Facility location, arising in a rich variety of applications, has been studied extensively in the fields of operations research and computer science. In this paper we consider the classical uncapacitated facility location problem and its “prize-collecting” variant introduced by Bäıou and Barahona, and we show that the linear systems associated with these problems are totally dual integral if an...
متن کاملTotal Dual Integrality in Some Facility Location Problems
Facility location, arising in a rich variety of applications, has been studied extensively in the fields of operations research and computer science. In this note we consider the classical uncapacitated facility location problem and its “prize-collecting” variant introduced by Bäıou and Barahona, and show that the linear systems associated with these problems are totally dual integral (TDI) if ...
متن کاملOn the Integrality of Some Facility Location Polytopes
We study a system of linear inequalities associated with some facility location problems. We show that this system defines a polytope with integer extreme points if and only if the graph does not contain a certain type of odd cycles. We also derive odd cycle inequalities and give a separation algorithm.
متن کامل1 Total Dual Integrality
1 Total Dual Integrality Recall that if A is TUM and b, c are integral vectors, then max{cx : Ax ≤ b} and min{yb : y ≥ 0, yA = c} are attained by integral vectors x and y whenever the optima exist and are finite. This gives rise to a variety of min-max results, for example we derived König’s theorem on bipartite graphs. There are many examples where we have integral polyhedra defined by a syste...
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In this paper we provide new characterizing properties of TDI systems, among others the following: A system of linear inequalities is TDI if and only if there exists a test set for its dual integer linear programs where all positive coordinates are equal to 1, and correspond to a set of linearly independent columns. Cook, Lovász and Schrijver’s result on the recognition – in polynomial time – o...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2012
ISSN: 0895-4801,1095-7146
DOI: 10.1137/090768400