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On the proper intervalization of colored caterpillar trees

Published online by Cambridge University Press:  30 July 2009

Carme Àlvarez  and
Maria Serna
Carme Àlvarez
Affiliation:
ALBCOM Research Group, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, C/ Jordi Girona Salgado 1-3, 08034 Barcelona, Spain; alvarez@lsi.upc.edu; mjserna@lsi.upc.edu
Maria Serna
Affiliation:
ALBCOM Research Group, Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord, Edifici Omega, C/ Jordi Girona Salgado 1-3, 08034 Barcelona, Spain; alvarez@lsi.upc.edu; mjserna@lsi.upc.edu
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Abstract

This paper studies the computational complexity of the proper interval colored graph problem (PICG), when the input graph is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the PICG and a graph layout problem the proper colored layout problem (PCLP). We show a dichotomy: the PICG and the PCLP are NP-complete for colored caterpillars of hair length ≥2, while both problems are in P for colored caterpillars of hair length <2. For the hardness results we provide a reduction from the multiprocessor scheduling problem, while the polynomial time results follow from a characterization in terms of forbidden subgraphs.

Keywords

Complexitycaterpillar treegraph layout problemscoloring
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 4 , October 2009 , pp. 667 - 686
Copyright
© EDP Sciences, 2009

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