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 conception, SWAT 2006, held in Riga, Latvia, in July 2006.
The lawsuits comprises 36 revised complete papers provided including three invited papers, addressing problems with theoretical algorithmics and functions in a number of fields together with graph algorithms, computational geometry, scheduling, approximation algorithms, community algorithms, information garage and manipulation, combinatorics, sorting, looking, on-line algorithms, optimization, amd more.
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Additional info for Algorithm Theory – SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006. Proceedings
Csirik. An online algorithm for variable-sized bin packing. Acta Informatica, 26:697–709, 1989. 7. J. Csirik and G. 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.
L ⊆ A. Furthermore, combining with Fact 1, we get 26 J. M. Favrholdt Fact 2. For any chain C and any item xi ∈ C, 2|xi | > |b|, for any bin b ∈ C. The total size of bins in F < \ F < is small: Note that the set F < \ F < of bins satisﬁes the conditions of Lemma 1, with β = α. Thus, |b| < 3M. , bo (xi ) = bo (xj ) = b. Then clearly, |xi | + |xj | ≤ |b|, contradicting Fact 2. Chains do not intersect: Assume for the sake of contradiction that there is a bin b contained in two chains C(x) and C(y), x = y.
Last opened) color if possible. If a new interval arrives that cannot be colored with the active color, this means that the maximum load is at least twice larger than the current guess. We therefore update the guess to equal twice the current guess, and open a new color with its capacity equal to twice the new value of the guess. Repeat this process until the interval can be colored with the most recently opened color. This color becomes active. Theorem 1. The competitive ratio of the above algorithm is 4.