Inverse booking problem: Inverse chromatic number problem in interval graphs

Yerim Chung, Jean François Culus, Marc Demange

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

We consider inverse chromatic number problems in interval graphs having the following form: we are given an integer K and an interval graph G = (V,E), associated with n = |V| intervals I i = ]a i ,b i [ (1 ≤ i ≤ n), each having a specified length s(I i ) = b i - a i , a (preferred) starting time a i and a completion time b i . The intervals are to be newly positioned with the least possible discrepancies from the original positions in such a way that the related interval graph can be colorable with at most K colors. We propose a model involving this problem called inverse booking problem.We show that inverse booking problems are hard to approximate within O(n 1 - ε ), ε > 0 in the general case with no constraints on lengths of intervals, even though a ratio of n can be achieved by using a result of [13]. This result answers a question recently formulated in [12] about the approximation behavior of the unweighted case of single machine just-in-time scheduling problem with earliness and tardiness costs. Moreover, this result holds for some restrictive cases.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - Second International Workshop, WALCOM 2008, Proceedings
Pages180-187
Number of pages8
DOIs
Publication statusPublished - 2008 Aug 27
Event2nd International Workshop on Algorithms and Computation, WALCOM 2008 - Dhaka, Bangladesh
Duration: 2008 Feb 72008 Feb 8

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4921 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Workshop on Algorithms and Computation, WALCOM 2008
CountryBangladesh
CityDhaka
Period08/2/708/2/8

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Chung, Y., Culus, J. F., & Demange, M. (2008). Inverse booking problem: Inverse chromatic number problem in interval graphs. In WALCOM: Algorithms and Computation - Second International Workshop, WALCOM 2008, Proceedings (pp. 180-187). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4921 LNCS). https://doi.org/10.1007/978-3-540-77891-2_17