منابع مشابه
Recognizing conic TDI systems is hard
In this note we prove that the problem of deciding whether or not a set of integer vectors forms a Hilbert basis is co-NP-complete. Equivalently, deciding whether a conic linear system is totally dual integral (TDI) or not, is co-NPcomplete. These are true even if the vectors in the set or respectively the coefficient vectors of the inequalities are 0−1 vectors having at most three ones.
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These are notes about Ding, Feng and Zang’s proof [5]. The proof of their result is not new, the only difference with them is the starting point: we work directly on their gadget graph encoding a SAT problem and not on more general graphs. This allows to shortcut some parts of the original proof that become superfluous. After proving their theorem I clarify some points about total dual integral...
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We consider only undirected graphs without loops or multiple edges. Our terminology and notation will be standard except as indicated; a good reference for any undefined terms is [2]. We will use c(G) to denote the number of components of a graph G. Chvtital introduced the notion of tough graphs in [3]. Let t be any positive real number. A graph G is said to be t-tough if tc(G-X)5 JXJ for all X...
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A recurring theme in the mathematical social sciences is how to select the “most desirable” elements given some binary dominance relation on a set of alternatives. Schwartz’s Tournament Equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context. Due to its unwieldy recursive definition, little is ...
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We define the notion of disk-obedience for a set of disks in the plane and give results for diskobedient graphs (DOGs), which are disk intersection graphs (DIGs) that admit a planar embedding with vertices inside the corresponding disks. We show that in general it is hard to recognize a DOG, but when the DIG is thin and unit (i.e., when the disks are unit disks), it can be done in linear time. ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2009
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-009-0294-5