Relaxations of combinatorial problems via association schemes
de Klerk,E. De Oliveira Filho,F.M. Pasechnik,D.V.
de Klerk,E.
De Oliveira Filho,F.M.
Pasechnik,D.V.
Abstract
In this chapter we describe a novel way of deriving semidefinite programming relaxations of a wide class of combinatorial optimization problems. Many combinatorial optimization problems may be viewed as finding an induced subgraph of a specific type of maximum weight in a given weighted graph. The relaxations we describe are motivated by concepts from algebraic combinatorics. In particular, we consider a matrix algebra that contains the adjacency matrix of the required subgraph, and formulate a convex relaxation of this algebra. Depending on the type of subgraph, this algebra may be the Bose–Mesner algebra of an association scheme, or, more generally, a coherent algebra. Thus we obtain new (and known) relaxations of the traveling salesman problem, maximum equipartition problems in graphs, the maximum stable set problem, etc.
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Pagination: 957
Date
2012
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Springer Verlag
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Citation
de Klerk, E, De Oliveira Filho, F M & Pasechnik, D V 2012, Relaxations of combinatorial problems via association schemes. in M F Anjos & J B Lasserre (eds), Handbook on Semidefinite, Conic and Polynomial Optimization. International Series in Operations Research & Management Science, no. 166, Springer Verlag, Berlin, pp. 171-200.
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