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
Performance testing of combinatorial solvers with isomorph class instances
Proceedings of the 2007 workshop on Experimental computer science
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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. Our conjecture is made more precise in two steps: (a) crossing minimization is used on a derived graph to achieve desirable permutations of rows and columns; and (b) the degree of randomness (lack of structure) is measured using diffusion, a measure that approximates what a human perceives as lack of structure. Additional experiments on synthetic instances related to the benchmarks add validity to our conjecture. We observe unexpectedly sharp thresholds where, with only slight variation of our measure, the dominance of the algorithms reverses dramatically. The nature of and explanation for this threshold behavior is left for future research as are many other questions. As far as we are aware the approach taken here is unique and, we hope, will inspire other research of its kind.