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ESA
2006
Springer

Finding Total Unimodularity in Optimization Problems Solved by Linear Programs

12 years 3 months ago
Finding Total Unimodularity in Optimization Problems Solved by Linear Programs
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally unimodular. Still, sometimes it is possible to build an integer solution with same cost from the fractional solution. Examples are two scheduling problems [3, 4] and the single disk prefetching/caching problem [2]. We show that problems such as the three previously mentioned can be separated into two subproblems: (1) finding an optimal feasible set of slots, and (2) assigning the jobs or pages to the slots. It is straigthforward to show that the latter can be solved greedily. We are able to solve the first with a totally unimodular linear program, which provides simpler (and sometimes combinatorial) algorithms with better worst case running times.
Christoph Dürr, Mathilde Hurand
Added 22 Aug 2010
Updated 22 Aug 2010
Type Conference
Year 2006
Where ESA
Authors Christoph Dürr, Mathilde Hurand
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