Tree-width and the Sherali-Adams operator

Authors:
Daniel Bienstock;Nuri Ozbay
Affiliations:
Department of Industrial Engineering & OR, Columbia University, New York, NY 10027, USA;Department of Industrial Engineering & OR, Columbia University, New York, NY 10027, USA
Venue:
Discrete Optimization
Year:
2004

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Abstract

We describe a connection between the tree-width of graphs and the Sherali-Adams reformulation procedure for 0/1 integer programs. For the case of vertex packing problems, our main result can be restated as follows: let G be a graph, let k=1 and let x@^@?R^V^(^G^) be a feasible vector for the formulation produced by applying the level-k Sherali-Adams algorithm to the edge formulation for STAB(G). Then for any subgraph H of G, of tree-width at most k, the restriction of x@^ to R^V^(^H^) is a convex combination of stable sets of H.