By Tetsuo Asano (auth.), Seok-Hee Hong, Hiroshi Nagamochi, Takuro Fukunaga (eds.)
This publication constitutes the refereed complaints of the nineteenth foreign Symposium on Algorithms and Computation, ISAAC 2008, held in Gold Coast, Australia in December 2008.
The seventy eight revised complete papers including three invited talks awarded have been rigorously reviewed and chosen from 229 submissions for inclusion within the booklet. The papers are geared up in topical sections on approximation algorithms, on-line algorithms, facts constitution and algorithms, online game thought, graph algorithms, mounted parameter tractability, dispensed algorithms, database, approximation algorithms, computational biology, computational geometry, complexity, networks, optimization in addition to routing.
Read Online or Download Algorithms and Computation: 19th International Symposium, ISAAC 2008, Gold Coast, Australia, December 15-17, 2008. Proceedings PDF
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Extra info for Algorithms and Computation: 19th International Symposium, ISAAC 2008, Gold Coast, Australia, December 15-17, 2008. Proceedings
1(a) (both solid and dotted edges). It models a situation in which power stations with ﬁxed capacity (the square vertices) provide power to customers with ﬁxed demand (the round vertices). It can be seen as a feasible solution of a particular instance of a search problem which we may call the power supply problem [10,11]: Given a bipartite graph G = (U, V, E) with weights on the vertices, is there a forest covering all vertices in G, and with exactly one vertex from U in each component, such that the sum of the demands of the V vertices (customers) in each component is no more than the capacity of the U vertex (power station) in it?
De Abstract. A coloring of the vertices of a graph is called convex if each subgraph induced by all vertices of the same color is connected. We consider three variants of recoloring a colored graph with minimal cost such that the resulting coloring is convex. Two variants of the problem are shown to be N P-hard on trees even if in the initial coloring each color is used to color only a bounded number of vertices. For graphs of bounded treewidth, we present a polynomial-time (2+ )-approximation algorithm for these two variants and a polynomial-time algorithm for the third variant.
If after these colorings there is at least one uncolored positive or negative vertex, we take for each such vertex y a new color cy and assign it to y as well as to exactly one uncolored free vertex. One can show that F is satisﬁable if and only if (T, C) has a convex recoloring C with cost ≤ 2nr+(n+2m). The proof of this equivalence is omitted. Although the MCRP is N P-complete when being restricted to initial (∞, 2)colorings, this is not the fact for the MRRP as we show in Theorem 6. However, a slight modiﬁcation of the reduction above shows that the MRRP on weighted graphs with an initial (∞, 4)-coloring is also N P-hard even for trees.
Algorithms and Computation: 19th International Symposium, ISAAC 2008, Gold Coast, Australia, December 15-17, 2008. Proceedings by Tetsuo Asano (auth.), Seok-Hee Hong, Hiroshi Nagamochi, Takuro Fukunaga (eds.)