By Dorothea Wagner (auth.), Takao Asano, Shin-ichi Nakano, Yoshio Okamoto, Osamu Watanabe (eds.)

This ebook constitutes the refereed lawsuits of the twenty second overseas Symposium on Algorithms and Computation, ISAAC 2011, held in Yokohama, Japan in December 2011. The seventy six revised complete papers provided including invited talks have been rigorously reviewed and chosen from 187 submissions for inclusion within the ebook. This quantity comprises issues equivalent to approximation algorithms; computational geometry; computational biology; computational complexity; information buildings; dispensed platforms; graph algorithms; graph drawing and data visualization; optimization; on-line and streaming algorithms; parallel and exterior reminiscence algorithms; parameterized algorithms; video game thought and web algorithms; randomized algorithms; and string algorithms.

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There is a polynomial time (O(log2 n), O(log n))-approximation for SLkST. More specifically, the algorithm finds a k-Steiner tree of diameter at most O(L · log n) whose cost is at most O(opt∗ · log2 n) where opt∗ is the cost of an LP relaxation of the problem. To prove this theorem we combine ideas from all of [3,5,6,12]. We first show that the algorithm of Marathe et al. [15] for SLST actually finds a solution with diameter at most O(L · log |T |) whose cost is at most O(opt∗ · log |T |), where opt∗ is the cost of a natural LP-relaxation, so we give a stronger bound (based on an LP relaxation) for the cost of their algorithm.

3 log n Note that 2−i · ki ≥ k. Consider an instance of classical survivable i=0 network design problem over terminals in Ti ∪ {r} with connectivity requirement 2 from every node in Ti to root. In the following lemma we show that we can compute a 2-edge-connected subgraph Hi over Ti ∪ {r} of cost at most O(2i · opt∗ ). This describes how to perform Step 7. 2 in [14]. Lemma 8. In Step 7, For each 0 ≤ i ≤ 3 log n , we can find a 2-edge-connected subgraph Hi of cost at most 2i+3 · opt∗ containing terminals Ti ∪ {r}.

ISAAC 2011, LNCS 7074, pp. 30–39, 2011. c Springer-Verlag Berlin Heidelberg 2011 Improved Approximation Algorithms for Routing Shop Scheduling 31 M1 , M2 , . . , Mm which originally stay at vertex 0, Job j consists of m operations O1,j , O2,j , . . , Om,j , where Oi,j should be processed by machine Mi for pi,j time units without any interruption. To process these jobs the machines travel between the vertices at the same speed. And the travel time between vertices j and k, denoted by tj,k , equals the length of the shortest path between them.

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