Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, April 09, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Gianpaolo Oriolo (Università degli Studi di Roma)

Large decomposition methods for independent sets in claw-free graphs

The (weighted) independent set problem in claw-free graphs is a fundamental generalization of the matching problem. In fact, claw-free graphs are a superclass of line graphs, and the (weighted) independent set problem in line graphs is equivalent to the (weighted) matching problem. Building upon the current state-of-the-art algorithm for the weighted matching problem (by Gabow), the weighted independent set problem in a line graph G(V,E) can be solved in time O(|V|^2 log(|V|)). In this talk, we will quickly surf through a few algorithms that have been proposed for the problem, starting from the classical algorithm from 1980 due to Minty, passing by the elegant algorithm for the unweighted case due Lov\'asz and Plummer in 1986. Our journey will take us to the current state-of-the-art algorithm for the problem, that exploits a decomposition technique due to Chudnovsky and Seymour and finds a maximum weighted independent set in a claw-free graph G(V,E) in time O(|V|^3). We will revise this powerful technique and discuss how to apply similar ideas to go beyond claw-free graphs or beyond the independent set problem.

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