18,437 research outputs found
The generalized minimum spanning tree polytope and related polytopes
The Generalized Minimum Spanning Tree problem denoted by GMST is a variant of the classical Minimum Spanning Tree problem in which nodes are partitioned into clusters and the problem calls for a minimum cost tree spanning at least one node from each cluster. A different version of the problem, called E-GMST arises when exactly one node from each cluster has to be visited. Both GMST problem and E-GMST problem are NP-hard problems. In this paper, we model GMST problem and E-GMST problem as integer linear programs and study the facial structure of the corresponding polytopes
Elementary equivalence versus Isomorphism
How does the first order language of fields encode birational invariants of
varieties?... This question is related to rational points on varieties and
effectiveness in algebraic/arithmetic geometry
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