research-article

Exact exponential algorithms to find tropical connected sets of minimum size

Authors:

Mathieu Chapelle,

Manfred Cochefert,

Dieter Kratsch,

Romain Letourneur,

Mathieu LiedloffAuthors Info & Claims

Theoretical Computer Science, Volume 676, Issue C

Pages 33 - 41

https://doi.org/10.1016/j.tcs.2017.03.003

Published: 09 May 2017 Publication History

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 SV 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.

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Cited By

Sampaio ILima K(2023)A Combinatorial Optimization Model and Polynomial Time Heuristic for a Problem of Finding Specific Structural Patterns in NetworksIntelligent Systems10.1007/978-3-031-45368-7_3(33-47)Online publication date: 25-Sep-2023
https://dl.acm.org/doi/10.1007/978-3-031-45368-7_3
Bliznets ISagunov DTagin E(2023)Enumeration of Minimal Tropical Connected SetsAlgorithms and Complexity10.1007/978-3-031-30448-4_10(127-141)Online publication date: 13-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-30448-4_10

Index Terms

Exact exponential algorithms to find tropical connected sets of minimum size
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
      2. Graph enumeration
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 676, Issue C

May 2017

49 pages

ISSN:0304-3975

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Copyright © Elsevier B.V.

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 09 May 2017

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Cited By

Sampaio ILima K(2023)A Combinatorial Optimization Model and Polynomial Time Heuristic for a Problem of Finding Specific Structural Patterns in NetworksIntelligent Systems10.1007/978-3-031-45368-7_3(33-47)Online publication date: 25-Sep-2023
https://dl.acm.org/doi/10.1007/978-3-031-45368-7_3
Bliznets ISagunov DTagin E(2023)Enumeration of Minimal Tropical Connected SetsAlgorithms and Complexity10.1007/978-3-031-30448-4_10(127-141)Online publication date: 13-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-30448-4_10

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