Approximating Incremental Combinatorial Optimization Problems

Authors Michel X. Goemans, Francisco Unda

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Michel X. Goemans
Francisco Unda

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Michel X. Goemans and Francisco Unda. Approximating Incremental Combinatorial Optimization Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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+sqrt(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.
  • Approximation algorithm
  • matching
  • incremental problems
  • matroid intersection
  • integral polytopes
  • stable sets


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