Algorithm Theory – SWAT 2006: 10th Scandinavian Workshop on by Raimund Seidel (auth.), Lars Arge, Rusins Freivalds (eds.)

By Raimund Seidel (auth.), Lars Arge, Rusins Freivalds (eds.)

This booklet constitutes the refereed court cases of the tenth Scandinavian Workshop on set of rules concept, SWAT 2006, held in Riga, Latvia, in July 2006.

The court cases comprises 36 revised complete papers offered including three invited papers, addressing problems with theoretical algorithmics and purposes in a number of fields together with graph algorithms, computational geometry, scheduling, approximation algorithms, community algorithms, info garage and manipulation, combinatorics, sorting, looking, on-line algorithms, optimization, amd more.

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Extra info for Algorithm Theory – SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006. Proceedings

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J. Woeginger. On-line packing and covering problems. In A. Fiat and G. J. Woeginger, editors, Online Algorithms: The State of the Art, LNCS 1442, pages 147–177, 1998. 8. L. Epstein and M. Levy. Online interval coloring and variants. In Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP’05), LNCS 3580, pages 602–613, 2005. 9. L. Epstein and M. Levy. Online interval coloring with packing constraints. In Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science (MFCS’05), LNCS 3618, pages 295–307, 2005.

References 1. J. Boyar and L. M. Favrholdt. Scheduling jobs on grid processors. Technical Report IMADA preprint PP-2006-6, University of Southern Denmark, 2006. 2. M. R. Garey, R. L. Graham, and J. D. Ullman. An analysis of some packing algorithms. In Combinatorial algorithms (Courant Computer Science Symposium 9), pages 39–47, 1972. 3. R. L. Graham. Bounds on multiprocessing anomalies and related packing algorithms. In Proc. 1972 Spring Joint Computer Conference, pages 205–217, 1972. 4. A. R. Karlin, M.

Favrholdt Proof. Let M = M 4 . Consider the following instance of the problem. Items: n items of size 2M + 1 and 2n items of size M + 1, for some even n. Bins: First, n bins of size 2M + 2. Let q, 0 ≤ q ≤ n, be the number of items of size 2M + 1 that the algorithm A packs in these bins. If q ≥ n2 , the sequence continues with 2n bins of size 2M + 1. If q < n2 , the sequence continues with 2n bins of size M + 1 and then n − q bins of size 4M . 3 First-Fit-Decreasing and a Better Variant Since the item sizes are known in advance, one can use an algorithm based on First-Fit-Decreasing for the standard off-line bin packing problem.

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