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# Exact Exponential Algorithms to Find a Tropical Connected Set of Minimum Size

Abstract : The input of the Tropical Connected Set problem is a vertex-colored graph G=(V,E) and the task is to find a connected subset $S\subseteq V$ 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.
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Conference papers

https://hal.archives-ouvertes.fr/hal-01105083
Contributor : Mathieu Liedloff Connect in order to contact the contributor
Submitted on : Monday, January 19, 2015 - 4:51:41 PM
Last modification on : Saturday, June 25, 2022 - 10:12:43 AM

### Citation

Mathieu Chapelle, Manfred Cochefert, Dieter Kratsch, Romain Letourneur, Mathieu Liedloff. Exact Exponential Algorithms to Find a Tropical Connected Set of Minimum Size. Parameterized and Exact Computation - 9th International Symposium, Sep 2014, Wroclaw, Poland. pp.147-158, ⟨10.1007/978-3-319-13524-3_13⟩. ⟨hal-01105083⟩

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