Approximating incremental combinatorial optimization problems
Author(s)Goemans, Michel X; Unda, Francisco Tomas
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We consider incremental combinatorial optimization problems, in which a solution is constructed incrementally over time, and the goal is to optimize not the value of the final solution but the average value over all timesteps. We consider a natural algorithm of moving towards a global optimum solution as quickly as possible. We show that this algorithm provides an approximation guarantee of (9 + √21)/15 > 0.9 for a large class of incremental combinatorial optimization problems defined axiomatically, which includes (bipartite and non-bipartite) matchings, matroid intersections, and stable sets in claw-free graphs. Furthermore, our analysis is tight.
DepartmentMassachusetts Institute of Technology. Department of Mathematics; Sloan School of Management
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RAN- DOM 2017)
Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing
Michel X. Goemans and Francisco Unda. "Approximating incremental combinatorial optimization problems." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017), Article No. 6; pp. 6:1–6:14.
Final published version
Approximation algorithm, matching, incremental problems, matroid intersection, integral polytopes, stable sets