Algorithms and Data Structures: 13th International by Mahmuda Ahmed, Iffat Chowdhury, Matt Gibson (auth.), Frank

By Mahmuda Ahmed, Iffat Chowdhury, Matt Gibson (auth.), Frank Dehne, Roberto Solis-Oba, Jörg-Rüdiger Sack (eds.)

This ebook constitutes the refereed court cases of the thirteenth Algorithms and information constructions Symposium, WADS 2013, held in London, ON, Canada, August 2013. The Algorithms and knowledge constructions Symposium - WADS (formerly "Workshop on Algorithms and knowledge Structures") is meant as a discussion board for researchers within the quarter of layout and research of algorithms and knowledge constructions. The forty four revised complete papers offered during this quantity have been rigorously reviewed and chosen from 139 submissions. The papers current unique examine on algorithms and information constructions in all parts, together with bioinformatics, combinatorics, computational geometry, databases, images, and parallel and disbursed computing.

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Additional info for Algorithms and Data Structures: 13th International Symposium, WADS 2013, London, ON, Canada, August 12-14, 2013. Proceedings

Sample text

There are at most n patterns P for which the primal variables xP are non-zero in the solution, implying that our algorithm returns a solution in which each rectangle is sliced at most n − 1 times. We also observe that in the solution produced by the FPTAS, the number of cuts per rectangle can be further reduced to a constant that depends only on ε. More precisely, we can show (details are omitted) that any feasible solution can be modified so that each rectangle is sliced at most (1/ε)O(1/ε) times, without increasing the height by more than a factor of 1 + O(ε).

So if A0R > (1 − α)HOPT W , then at some point during the shifting process we reach a moment when AR = (1 − α)HOPT W as desired. Step 3. Pack the left pieces into the left strip and the right pieces into the right strip, using Shelf on both sides. Theorem 2. There exists a 5/3-approximation for 2SP-SSC that slices every rectangle at most three times and runs in time O(n log (nM )), where M is an upper bound on the integer heights of the rectangles. Proof. Assume for now that HOPT is known and apply the above algorithm.

A review of machine scheduling: complexity, algorithms and approximability. In: Handbook of Combinatorial Optimization, vol. 3, pp. 21–169. Kluwer Acad. , Boston (1998) 4. : Performance bounds for level-oriented two-dimensional packing algorithms. SIAM J. Comput. 9(4), 808– 826 (1980) 5. : Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman & Co. Ltd. (1979) 6. : A linear programming approach to the cutting-stock problem. Operations Res. 9, 849–859 (1961) 7. : Our energy future and smart grid communications.

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