Exact exponential algorithms to find tropical connected sets of minimum size

Tropical Connected Set is strongly related to the Graph Motif problem which deals with vertex-colored graphs. Graph Motif has various applications in biology and metabolic networks, and has widely been studied in the last twenty years. The input of the Tropical Connected Set problem is a vertex-colo...

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Published in:	Theoretical computer science Vol. 676; pp. 33 - 41
Main Authors:	Chapelle, Mathieu, Cochefert, Manfred, Kratsch, Dieter, Letourneur, Romain, Liedloff, Mathieu
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 09.05.2017 Elsevier
Subjects:	Algorithms Colored graphs Computer Science Data Structures and Algorithms Exact exponential algorithms Graphs Exact exponential algorithms Graphs Algorithms Colored graphs
ISSN:	0304-3975, 1879-2294
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Abstract	Tropical Connected Set is strongly related to the Graph Motif problem which deals with vertex-colored graphs. Graph Motif has various applications in biology and metabolic networks, and has widely been studied in the last twenty years. The input of the Tropical Connected Set problem is a vertex-colored graph (G,c), where G=(V,E) is a graph and c is a vertex coloring assigning to each vertex of G a color. 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 study 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. We also show that Tropical Connected Set on trees has no sub-exponential algorithm unless the Exponential Time Hypothesis fails.
AbstractList	Tropical Connected Set is strongly related to the Graph Motif problem which deals with vertex-colored graphs. Graph Motif has various applications in biology and metabolic networks, and has widely been studied in the last twenty years. The input of the Tropical Connected Set problem is a vertex-colored graph (G,c), where G=(V,E) is a graph and c is a vertex coloring assigning to each vertex of G a color. 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 study 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. We also show that Tropical Connected Set on trees has no sub-exponential algorithm unless the Exponential Time Hypothesis fails.
Author	Letourneur, Romain Liedloff, Mathieu Chapelle, Mathieu Cochefert, Manfred Kratsch, Dieter
Author_xml	– sequence: 1 givenname: Mathieu surname: Chapelle fullname: Chapelle, Mathieu email: Mathieu.ch@gmail.com organization: Université Libre de Bruxelles, CP 212, 1050 Bruxelles, Belgium – sequence: 2 givenname: Manfred surname: Cochefert fullname: Cochefert, Manfred email: manfred.cochefert@univ-lorraine.fr organization: Université de Lorraine, LITA, 57045 Metz cedex 01, France – sequence: 3 givenname: Dieter surname: Kratsch fullname: Kratsch, Dieter email: dieter.kratsch@univ-lorraine.fr organization: Université de Lorraine, LITA, 57045 Metz cedex 01, France – sequence: 4 givenname: Romain surname: Letourneur fullname: Letourneur, Romain email: romain.letourneur@univ-orleans.fr organization: Université d'Orléans, INSA Centre Val de Loire, LIFO, 45067 Orléans, France – sequence: 5 givenname: Mathieu surname: Liedloff fullname: Liedloff, Mathieu email: mathieu.liedloff@univ-orleans.fr organization: Université d'Orléans, INSA Centre Val de Loire, LIFO, 45067 Orléans, France
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SubjectTerms	Algorithms Colored graphs Computer Science Data Structures and Algorithms Exact exponential algorithms Graphs
Title	Exact exponential algorithms to find tropical connected sets of minimum size
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