Download e-book for iPad: Algorithms and Computation: 22nd International Symposium, by Dorothea Wagner (auth.), Takao Asano, Shin-ichi Nakano,

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

This e-book constitutes the refereed court cases 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 offered including invited talks have been conscientiously reviewed and chosen from 187 submissions for inclusion within the ebook. This quantity comprises subject matters resembling approximation algorithms; computational geometry; computational biology; computational complexity; info constructions; dispensed platforms; graph algorithms; graph drawing and knowledge visualization; optimization; on-line and streaming algorithms; parallel and exterior reminiscence algorithms; parameterized algorithms; online game thought and net algorithms; randomized algorithms; and string algorithms.

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Read or Download Algorithms and Computation: 22nd International Symposium, ISAAC 2011, Yokohama, Japan, December 5-8, 2011. Proceedings PDF

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2 Related Work There are an enormous number of results concerning vehicle routing problems; see the survey [12]. The Capacitated Vehicle Routing Problem (CVRP) enforces a limit C on the number of visited locations in each route, and the goal is the minimization of the total length of all the routes. The paper [5] established a strong link to the underlying Travelling Salesman Problem (TSP) by giving an approximation algorithm that relies on the approximation algorithms for TSP. Depending on the capacity bound C, it is possible to obtain a PTAS in the euclidean plane for some special cases (if the capacity is either small [1], or very large [2]).

It is easy to see that this formulation is a special case of buy-at-bulk since a linear function (defined based on c and ) is also sub-additive. It turns out that an α-approximation for the cost-distance version implies a (2α + )-approximation algorithm for the buy-at-bulk version too (see [1,5,16]). For simplicity, we focus on the two cost function (cost+distance) formulation of buy-at-bulk from now on. Network optimization problems with multiple cost functions, such as buy-atbulk network design problems, have been studied extensively because of their applications.

Lemma 3. One can find a mapping φ : J −→ A from junction points to anchors in polynomial time with the following properties: (i) For all j ∈ J, the junction point j lies on the path P (s, φ(j)); (ii) For all a ∈ A, there is at most one junction point j ∈ J with φ(j) = a. s r(S) t(S) S b(S) For every core segment S, let t(S) and b(S) be the top and the bottom junction points in S. Let further r(S) be the highest junction point at distance at most R/2 from t(S) (see Fig. at side). Our algorithm works as follows.

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