Linear programming: methods and applications (5th ed.)
Linear programming: methods and applications (5th ed.)
Set Covering by an All Integer Algorithm: Computational Experience
Journal of the ACM (JACM)
Synthesis and Optimization of Digital Circuits
Synthesis and Optimization of Digital Circuits
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Decomposing Matrices into Blocks
SIAM Journal on Optimization
Heuristics, Experimental Subjects, and Treatment Evaluation in Bigraph Crossing Minimization
Journal of Experimental Algorithmics (JEA)
Permuting Sparse Rectangular Matrices into Block-Diagonal Form
SIAM Journal on Scientific Computing
On SAT Instance Classes and a Method for Reliable Performance Experiments with SAT Solvers
Annals of Mathematics and Artificial Intelligence
Effective bounding techniques for solving unate and binate covering problems
Proceedings of the 42nd annual Design Automation Conference
Search pruning techniques in SAT-based branch-and-bound algorithms for the binate covering problem
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Journal of Experimental Algorithmics (JEA)
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After extensive experiments with two algorithms, CPLEX and our implementation of all-integer dual simplex, we observed extreme differences between the two on a set of design automation benchmarks. In many cases one of the two would find an optimal solution within seconds while the other timed out at one hour. We conjecture that this contrast is accounted for by the extent to which the constraint matrix can be made block diagonal via row/column permutations. The actual structure of the matrix without the permutations is not important. We used crossing minimization to discover the right permutations that make the underlying structure, whether block diagonal or random, visible. Our conjecture leads to a testable hypothesis for a limited domain. The hypothesis is based on earlier observations reported in an earlier version of this paper and subsequent exploratory experiments. We present a sample of the results validating the hypothesis and make additional observations outside its scope. As far as we are aware the approach taken here is unique and, we hope, will inspire other research of its kind.