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Eun Jung Kim (김은정), New algorithm for multiway cut guided by strong min-max duality
Friday, January 4, 2019 @ 4:00 PM - 5:00 PM KST
Problems such as Vertex Cover and Multiway Cut have been well-studied in parameterized complexity. Cygan et al. 2011 drastically improved the running time of several problems including Multiway Cut and Almost 2SAT by employing LP-guided branching and aiming for FPT algorithms parameterized above LP lower bounds. Since then, LP-guided branching has been studied in depth and established as a powerful technique for parameterized algorithms design.
In this talk, we make a brief overview of LP-guided branching technique and introduce the latest results whose parameterization is above even stronger lower bounds, namely μ(I)=2LP(I)-IP(dual-I). Here, LP(I) is the value of an optimal fractional solution and IP(dual-I) is the value of an optimal integral dual solution. Tutte-Berge formula for Maximum Matching (or equivalently Edmonds-Gallai decomposition) and its generalization Mader’s min-max formula are exploited to this end. As a result, we obtain an algorithm running in time 4k-μ(I) for multiway cut and its generalizations, where k is the budget for a solution.
This talk is based on a joint work with Yoichi Iwata and Yuichi Yoshida from NII.