Abstract
We correct a result that we recently published in this conference series on the polytope of Binary Constraint Problems (BCPs). We had claimed that the so-called ”support formulation” would characterize the convex hull of all feasible solutions to tree-structured BCPs. We show that this claim is not accurate by providing a small counter example. We then show that the respective polytope defines a facet of the stable-set polytope of a perfect graph which allows us to perform LP inference in polynomial time.
This work was supported by the National Science Foundation through the Career: Cornflower Project (award number 0644113).
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References
Aron, I.D., Leventhal, D.H., Sellmann, M.: A Totally Unimodular Description of the Consistent Value Polytope for Binary Constraint Programming. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 16–28. Springer, Heidelberg (2006)
Chudnovsky, M., Robertson, N., Seymour, P.D., Thomas, R.: Progress on Perfect Graphs. Mathematical Programming 97, 405–422 (2003)
Chvatal, V.: On certain polytopes associated with graphs. Combinatorial Theory B 18, 138–154 (1975)
Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artificial Intelligence 38, 353–366 (1989)
Freuder, E.C.: Complexity of k-tree structured constraint satisfaction problems. In: AAAI, pp. 4–9 (1990)
Sellmann, M., Mercier, L., Leventhal, D.H.: The Linear Programming Polytope of Binary Constraint Problems with Bounded Tree-Width. In: CPAIOR, pp. 275–287 (2007)
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Sellmann, M. (2008). The Polytope of Tree-Structured Binary Constraint Satisfaction Problems. In: Perron, L., Trick, M.A. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2008. Lecture Notes in Computer Science, vol 5015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68155-7_39
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DOI: https://doi.org/10.1007/978-3-540-68155-7_39
Publisher Name: Springer, Berlin, Heidelberg
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