Approximating incremental combinatorial optimization problems
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Author(s)
Goemans, Michel X
Unda, Francisco Tomas
Date Issued
August 2017
Journal
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RAN- DOM 2017)
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing
Citation
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.
Version
Final published version
Abstract
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.
Subjects
Approximation algorithm, matching, incremental problems, matroid intersection, integral polytopes, stable sets
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Sloan School of Management
Terms of Use
Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2017.6
