Geodesic
Reducing Off-Line to On-Line: an Example and Its Applications
Yugoslav journal of operations research, Tome 13 (2003) no. 1, p. 3 .

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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 - 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 off- line one.
Classification : 68R10 90C27
Keywords: Combinatorial problems, on-line computation, reductions, hereditary subgraph 
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Marc Demange. Reducing Off-Line to On-Line: an Example and Its Applications. Yugoslav journal of operations research, Tome 13 (2003) no. 1, p. 3 . http://geodesic.mathdoc.fr/item/YJOR_2003_13_1_a0/