A structural approach to kernels for ILPs
| Autor: | Jansen, B.M.P., Kratsch, S., Bansal, N., Finocchi, I. |
|---|---|
| Přispěvatelé: | Algorithms |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Mathematical optimization
021103 operations research 0211 other engineering and technologies Structure (category theory) Contrast (statistics) 0102 computer and information sciences 02 engineering and technology 01 natural sciences Tree decomposition Treewidth 010201 computation theory & mathematics Kernelization Preprocessor Constraint matrix Structural approach Mathematics |
| Zdroj: | Algorithms-ESA 2015 ISBN: 9783662483497 ESA Algorithms-ESA 2015 : 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, 779-791 STARTPAGE=779;ENDPAGE=791;TITLE=Algorithms-ESA 2015 : 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings |
| ISSN: | 0302-9743 |
| DOI: | 10.1007/978-3-662-48350-3_65 |
| Popis: | Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous work studied the existence of kernelizations for ILP related problems, e.g., for testing feasibility of Ax¿=¿b. In contrast to the observed success of CPLEX, however, the results were largely negative. Intuitively, practical instances have far more useful structure than the worst-case instances used to prove these lower bounds. In the present paper, we study the effect that subsystems that have (a Gaifman graph of) bounded treewidth or that are totally unimodular have on the kernelizability of the ILP feasibility problem. We show that, on the positive side, if these subsystems have a small number of variables on which they interact with the remaining instance, then we can efficiently replace them by smaller subsystems of size polynomial in the domain without changing feasibility. Thus, if large parts of an instance consist of such subsystems, then this yields a substantial size reduction. Complementing this we prove that relaxations to the considered structures, e.g., larger boundaries of the subsystems, allow worst-case lower bounds against kernelization. Thus, these relaxed structures give rise to instance families that cannot be efficiently reduced, by any approach. |
| Databáze: | OpenAIRE |
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