Solving Covering Problems Using LPR-based Lower Bounds

Unate and binate covering problems are a special class ofgeneral integer linear programming problems with which several problemsin logic synthesis, such as two-level logic minimization and technologymapping, are formulated. Previous branch-and-bound methodsfor exactly solving these problems use lower-bounding techniques basedon finding maximal independent sets. In this paper we examine lower-boundingtechniques based on linear programming relaxation (LPR) forthe binate covering problem. We show that a combination of traditionalreductions (essentiality and dominance) and incremental computation ofLPR-based lower bounds can exactly solve difficult covering problemsorders of magnitude faster than traditional methods.

[1]  Willard Van Orman Quine,et al.  A Way to Simplify Truth Functions , 1955 .

[2]  W. Quine.  On Cores and Prime Implicants of Truth Functions , 1959 .

[3]  Fabrizio Luccio,et al.  A Method for Minimizing the Number of Internal States in Incompletely Specified Sequential Networks , 1965, IEEE Trans. Electron. Comput..

[4]  James F. Gimpel.  A Reduction Technique for Prime Implicant Tables , 1964, IEEE Trans. Electron. Comput..

[5]  James F. Gimpel.  The Minimization of TANT Networks , 1967, IEEE Trans. Electron. Comput..

[6]  Nripendra N. Biswas,et al.  Minimization of Boolean Functions , 1971, IEEE Transactions on Computers.

[7]  J. Beasley.  An algorithm for set covering problem , 1987 .

[8]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[9]  Alberto Sangiovanni-Vincentelli,et al.  Logic synthesis for vlsi design , 1989 .

[10]  Srinivas Devadas,et al.  Exact algorithms for output encoding, state assignment, and four-level Boolean minimization , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[11]  Kurt Keutzer,et al.  Instruction selection using binate covering for code size optimization , 1995, ICCAD.

[12]  P. Barth.  A Davis-Putnam based enumeration algorithm for linear pseudo-Boolean optimization , 1995 .

[13]  Kurt Keutzer,et al.  Instruction selection using binate covering for code size optimization , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[14]  Olivier Coudert,et al.  New Ideas for Solving Covering Problems , 1995, 32nd Design Automation Conference.

[15]  Olivier Coudert,et al.  On solving covering problems , 1996, DAC '96.

[16]  Tiziano Villa,et al.  Negative thinking in search methods: application to unate covering , 1997, International Conference on Computer Aided Design.