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

This booklet constitutes the refereed lawsuits of the sixth Scandinavian Workshop on set of rules idea, SWAT'98, held in Stockholm, Sweden, in July 1998.
The quantity offers 28 revised complete papers chosen from fifty six submissions; additionally incorporated are 3 invited contributions. The papers current unique learn on algorithms and information buildings in a number of parts together with computational geometry, parallel and disbursed platforms, graph idea, approximation, computational biology, queueing, Voronoi diagrams, and combinatorics in general.

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

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Lueker, Bin packing can be solved within 1 + in linear time, Combinatorica, 1 (1981) 349 – 355. 38, 38, 38, 38, 39 7. R. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, San Francisco, 1979. 36 8. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, London, 1980. 35 9. S. Irani, Coloring inductive graphs on-line, Algorithmica, 11 (1994) 53 – 72. 37 10. S. Irani and V. Leung, Scheduling with conflicts, and applications to traffic signal control, Symposium on Discrete Algorithms, SODA 96, 85 – 94.

Hence if the ρ-approximation algorithm returns a solution of cost more than ρ then the 3DM instance has no solution. Let S be the solution of cost at most ρ returned by the ρ-approximation algorithm. We show that S is also a solution to the 3DM instance. Let a ∈ A. Let u be a triple for which u(1) = a (if such a triple does not exist then we already know that the 3DM instance has no solution). Since u must be covered at distance at most ρ at time-slot 1, and since all the edges at any time-slot are of length 1 or ρ + , there exists a triple v ∈ S such that v(1) = a.

We build a forest W with vertex set V = {aij |yij is in ci , 1 ≤ i ≤ m} and labelling (aij ) = i for 1 ≤ i ≤ m. The edge set E is given as follows: for each variable xk connect the vertices aij and ai j , if and only if yij = xk , yi j = x¯k and (i, j) = (i , j ). Using the property of the variables above, W forms a forest. Then, we can prove that α is satisfiable, if and only if there is an independent set of size m with labels 1, . . , m Our method is based on the following idea: if we have enough vertices in a d-inductive graph, then we can find an independent set with labels 1, .

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