Reducing off-line to on-line: An example and its applications

• Main Author: Demange Marc
• Format: Article
• Language: English
• Published: University of Belgrade 2003-01-01
• Series: Yugoslav Journal of Operations Research
• Subjects: combinatorial problems; on-line computation; reductions; hereditary subgraph problem
• Online Access: http://www.doiserbia.nb.rs/img/doi/0354-0243/2003/0354-02430301003D.pdf

We study on-line versions of maximum weighted hereditary subgraph problems for which the instance is revealed in two clusters. We focus on the comparison of these on-line problems with their respective off-line versions. In [3], we have reduced on-line versions to the off-line ones in order to devise competitive analysis for such problems. In this paper, we first devise hardness results pointing out that this previous analysis was tight. Then, we propose a process that allows, for a large class of hereditary problems, to transform an on-line algorithm into an off-line one with improvement of the guarantees. This result can be seen as an inverse version of our previous work. It brings to the fore a hardness gap between on-line and off-line versions of those problems. This result does not apply in the case of maximizing a k -colorable induced subgraph of a given graph. For this problem we point out that, contrary to the first case, the on-line version is almost as well approximated as the offline one. .