By David Eppstein (auth.), Otfried Cheong, Kyung-Yong Chwa, Kunsoo Park (eds.)
This ebook constitutes the refereed court cases of the twenty first overseas Symposium on Algorithms and Computation, ISAAC 2010, held in Jeju, South Korea in December 2010. The seventy seven revised complete papers awarded have been conscientiously reviewed and chosen from 182 submissions for inclusion within the booklet. This quantity includes subject matters equivalent to approximation set of rules; complexity; information constitution and set of rules; combinatorial optimization; graph set of rules; computational geometry; graph coloring; fastened parameter tractability; optimization; on-line set of rules; and scheduling.
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Extra info for Algorithms and Computation: 21st International Symposium, ISAAC 2010, Jeju Island, Korea, December 15-17, 2010, Proceedings, Part I
1 Introduction Given a graph with lengths on edges, the Generalized Steiner Tree Problem asks for the minimum length subgraph that connects given set of pairs of vertices. The first nontrivial approximation ratio of 2 has been given in  and for two decades there were no improvements of this ratio for any sufficiently wide subclass of graphs for which the problem is MAX SNP-hard. Note that as the Steiner tree problem, geometric cases admit PTAS . 25-approximation of Steiner trees in such graphs .
Approximate tandem repeats deals with diﬀerent metrics and diﬀers from the natural problem of approximate periodicity that we deﬁne. A natural way of handling errors is the following. , what is the smallest period that deﬁnes the given string with the smallest number of errors. It is natural to ask if such an approximate period can be found eﬃciently. The error cause varies with the diﬀerent phenomena. This is formalized by considering diﬀerent distance metrics. In this paper we study approximate periodicity under two metrics: the Hamming distance and the swap distance.
Note that as the Steiner tree problem, geometric cases admit PTAS . 25-approximation of Steiner trees in such graphs . In this paper we generalize ”potential technique” introduced in  to obtain a better factor for Generalized Steiner tree Problem. The resulted 3/2approximation algorithm is fairly simple but requires an elaborate nontrivial analysis. In the next section we formulate the Generalized Steiner tree problem and introduce necessary notations. In Section 3 we describe our approximation algorithm and in Section 4 we prove the approximation ratio of 3/2.