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Exact exponential algorithms to find a tropical connected set of minimum size

par Chapelle, Mathieu ;Cochefert, Manfred;Kratsch, Dieter;Letourneur, Romain;Liedloff, Mathieu
Référence Lecture notes in computer science, 8894, page (147-158)
Publication Publié, 2014

Article révisé par les pairs

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Résumé :

The input of the Tropical Connected Set problem is a vertexcolored graph G = (V, E) and the task is to find a connected subset S ⊆ V of minimum size such that each color of G appears in S. This problem is known to be NP-complete, even when restricted to trees of height at most three. We show that Tropical Connected Set on trees has no subexponential-time algorithm unless the Exponential Time Hypothesis fails. This motivates the study of exact exponential algorithms to solve Tropical Connected Set. We present an O∗(1.5359n) time algorithm for general graphs and an O∗(1.2721n) time algorithm for trees.