Supernode processing of mixed-integer models
Computational Optimization and Applications - Special issue dedicated to George Dantzig
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Presolving in linear programming
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Solving the Simple Plant Location Problem using a Data Correcting Approach
Journal of Global Optimization
General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Clustering For Data Mining: A Data Recovery Approach (Chapman & Hall/Crc Computer Science)
Clustering For Data Mining: A Data Recovery Approach (Chapman & Hall/Crc Computer Science)
Computational study of large-scale p-Median problems
Mathematical Programming: Series A and B
The Optimal Diversity Management Problem
Operations Research
Minimum Leaf Out-Branching Problems
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Data aggregation for p-median problems
Journal of Combinatorial Optimization
INOC'11 Proceedings of the 5th international conference on Network optimization
Flexible PMP Approach for Large-Size Cell Formation
Operations Research
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The paper is aimed at experimental evaluation of the complexity of the p-Median problem instances, defined by mxn costs matrices, from several of the most widely used libraries. The complexity is considered in terms of possible problem size reduction and preprocessing, irrespective of the solution algorithm. We use a pseudo-Boolean representation of PMP instances that allows several reduction techniques to be applied in a straightforward way: combining similar monomials in the polynomial, truncation of the polynomial from degree (m-1) to (m-p) implying costs matrix truncation and exclusion of some rows from the costs matrix (preprocessing based only on compactification of the costs matrix), decomposition of the polynomial into the minimum number of expressions inducing the minimum number of aggregated columns (reduction of the columns' number in the costs matrix). We show that the reduced instance has at most @?"i"="1^m^-^pmin{n,mi}+1 nonzero entries. We also provide results of computational experiments with the mentioned reductions that allow classification of the benchmark data complexity. Finally, we propose a new benchmark library of instances not amenable to size reduction by means of data compactification.