• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Parameterized complexity and approximation issues for the colorful components problems

Dondi, Riccardo; Sikora, Florian (2018), Parameterized complexity and approximation issues for the colorful components problems, Theoretical Computer Science, 739, p. 1-12. 10.1016/j.tcs.2018.04.044

View/Open
155324649282492.pdf (221.2Kb)
Type
Article accepté pour publication ou publié
Date
2018
Journal name
Theoretical Computer Science
Volume
739
Publisher
Elsevier
Pages
1-12
Publication identifier
10.1016/j.tcs.2018.04.044
Metadata
Show full item record
Author(s)
Dondi, Riccardo

Sikora, Florian cc
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful Components (MCC) and Maximum Edges in transitive Closure (MEC), introduced in 2011 in the context of orthology gene identification in bioinformatics. The input of both MCC and MEC is a vertex-colored graph. MCC asks for the removal of a subset of edges, so that the resulting graph is partitioned in the minimum number of colorful connected components; MEC asks for the removal of a subset of edges, so that the resulting graph is partitioned in colorful connected components and the number of edges in the transitive closure of such a graph is maximized. We study the parameterized and approximation complexity of MCC and MEC, for general and restricted instances.For MCC on trees we show that the problem is basically equivalent to Minimum Cut on Trees, thus MCC is not approximable within factor 1.36−ε, it is fixed-parameter tractable and it admits a poly-kernel (when the parameter is the number of colorful components). Moreover, we show that MCC, while it is polynomial time solvable on paths, it is NP-hard even for graphs with constant distance to disjoint paths number. Then we consider the parameterized complexity of MEC when parameterized by the number k of edges in the transitive closure of a solution (the graph obtained by removing edges so that it is partitioned in colorful connected components). We give a fixed-parameter algorithm for MEC parameterized by k and, when the input graph is a tree, we give a poly-kernel.
Subjects / Keywords
Colorful components; Parameterized complexity; Algorithms; Computational biology

Related items

Showing items related by title and author.

  • Thumbnail
    Parameterized Complexity and Approximation Issues for the Colorful Components Problems 
    Dondi, Riccardo; Sikora, Florian (2016) Communication / Conférence
  • Thumbnail
    The Longest Run Subsequence Problem: Further Complexity Results 
    Sikora, Florian; Dondi, Riccardo (2021) Communication / Conférence
  • Thumbnail
    Covering with Clubs: Complexity and Approximability 
    Dondi, Riccardo; Mauri, Giancarlo; Sikora, Florian; Zoppis, Italo (2018) Communication / Conférence
  • Thumbnail
    Parameterized exact and approximation algorithms for maximum k-set cover and related satisfiability problems 
    Bonnet, Édouard; Paschos, Vangelis; Sikora, Florian (2016) Article accepté pour publication ou publié
  • Thumbnail
    Parameterized and approximation complexity of Partial VC Dimension 
    Bazgan, Cristina; Foucaud, Florent; Sikora, Florian (2019) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo