Linear 0-1 Inequalities and Extended Clauses

Barth, Peter

doi:10.1007/3-540-56944-8_40

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Linear 0-1 Inequalities and Extended Clauses

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Barth, Peter
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Barth, P. (1993). Linear 0-1 Inequalities and Extended Clauses. In A. Voronkov (Ed.), Logic Programming and Automated Reasoning (pp. 40-51). Berlin, Germany: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-ADDF-9

Abstract

Extended clauses are the basic formulas of the 0-1 constraint solver used in
the constraint logic programming language CLP($\cal PB$). We present a method
for transforming an arbitrary linear 0-1 inequality into a set of extended
clauses, such that the solution space remains invariant. The method relies on
cutting planes techniques known from integer programming. We develop special
redundancy criteria and can so produce the minimal number of extended clauses.
We show how the algorithm can be used to replace the resolution rule in the
generalized resolution algorithm for extended clauses. Furthermore the method
can be used to obtain all strongest extended cover inequalities of a knapsack
inequality.