By Andrew V. Goldberg (auth.), Stefan Arnborg, Lars Ivansson (eds.)

ISBN-10: 3540646825

ISBN-13: 9783540646822

This booklet constitutes the refereed lawsuits of the sixth Scandinavian Workshop on set of rules thought, SWAT'98, held in Stockholm, Sweden, in July 1998.

The quantity provides 28 revised complete papers chosen from fifty six submissions; additionally incorporated are 3 invited contributions. The papers current unique study on algorithms and knowledge constructions in a variety of components together with computational geometry, parallel and dispensed platforms, graph conception, approximation, computational biology, queueing, Voronoi diagrams, and combinatorics in general.

**Read or Download Algorithm Theory — SWAT'98: 6th Scandinavian Workshop on Algorithm Theory Stockholm, Sweden, July 8–10, 1998 Proceedings PDF**

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**Additional info for Algorithm Theory — SWAT'98: 6th Scandinavian Workshop on Algorithm Theory Stockholm, Sweden, July 8–10, 1998 Proceedings**

**Sample text**

Furthermore, if j∈V sj ≤ 1 then we obtain the problem to compute the chromatic number χ(G) of the conflict graph G. This means that the bin packing problem with conflicts is NP-complete even if E = ∅ or if j∈V sj ≤ 1. 5 for the bin packing problem, unless P = N P . This is obvious since such an algorithm could be used to solve the partition problem [7] in polynomial time. For a survey about the bin packing problem we refer to [4]. The packing problem for an arbitrary undirected graph is harder to approximate, because Feige and Kilian [5] proved that it is hard to approximate the chromatic number to within Ω(|V |1− ) for any > 0, unless N P ⊂ ZP P .

If β ≥ 2d, then we obtain the upper bound |Iδ | ≤ 2d 1δ . In this case, we compute a (d + 1) coloring for the items in Iδ . Since all items vj ∈ Iδ have sizes at most δ, we can place at least 1δ of these items into one bin. Using a next fit heuristic for each color set, we obtain at most 3d + 1 bins for the items in Iδ . In total, we obtain in this case at most β + 3d + 1 bins. If β ≤ 2d, we have at least β − 2d bins with sizes larger than 1 − δ. The remaining jobs in Iδ can be packed (using a (d + 1) - coloring and NF for each color set) such that at most d + 1 further bins with sizes ≤ 1 − δ are generated.

This corresponds to partitioning the matrix onto parallel processors so as to minimize processor load while maintaining regular communication patterns. Applications of the problem include various parallel sparse matrix computations, compilers for high-performance languages, particle in cell computations, video and image compression, and simulations associated with a communication network. We analyze the performance guarantee of a natural and practical heuristic based on iterative refinement, which has previously been shown to give good empirical results.