By Pankaj K. Agarwal (auth.), Takeshi Tokuyama (eds.)

ISBN-10: 3540771182

ISBN-13: 9783540771180

This publication constitutes the refereed court cases of the 18th foreign Symposium on Algorithms and Computation, ISAAC 2007, held in Sendai, Japan, in December 2007.

The seventy seven revised complete papers provided including 2 invited talks have been rigorously reviewed and chosen from 220 submissions. The papers are geared up in topical sections on graph algorithms, computational geometry, complexity, graph drawing, allotted algorithms, optimization, info constitution, video game thought, database purposes, on-line algorithms, I/O algorithms, networks, geometric functions, and string.

**Read or Download Algorithms and Computation: 18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007. Proceedings PDF**

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**Additional resources for Algorithms and Computation: 18th International Symposium, ISAAC 2007, Sendai, Japan, December 17-19, 2007. Proceedings**

**Sample text**

For a subset X ⊆ V , the hypergraph G X induced by X is deﬁned to be an edge-weighted hypergraph (X, AX ∪ BX ) with an edge weight function wX : E → + such that AX = {e ∈ E | e ⊆ X}, BX = {e − X | e ∈ E, e − X = ∅, |e ∩ X| ≥ 2}, wX (e) = w(e) if e ∈ AX w(e)/2 if e ∈ BX . , |e| = 2, e ∈ E) then BX = ∅. Then we can obtain the following (the proof is omitted for space reasons). Lemma 2. For an edge-weighted hypergraph (G = (V, E), w), an ordering π = (v1 , v2 , . . , vn ) such that d(G V−Vi−1 ,wV−Vi−1 ) (vi ) = min{d(G | v ∈ V − Vi−1 }, i = 1, 2, .

If f is symmetric and crossing submodular or intersecting submodular and posi-modular, then the family X (f ) of extreme subsets of f can be found in O(n3 Tf ) time. An important example of symmetric and fully submodular functions is the cut functions of hypergraphs. Let (G = (V, E), w) be a hypergraph with vertex set V , hyperedge set E (⊆ 2V −({∅}∪{{v} | v ∈ V })) and weight function w : E → + . The cut function of (G, w) is deﬁned by d(G,w) : 2V → + such that d(G,w) (X) = {w(e) | e ∈ E, e ∩ X = ∅ = e − X}, (10) where we let d(G,w) (∅) = d(G,w) (V ) = 0.

1 Introduction Problems of selecting the best location of facilities in a given network to satisfy a certain property are called location problems [11]. Recently, the location problems with requirements measured by a network-connectivity have been studied extensively [2, 3, 5, 7, 6, 9, 10, 13, 14, 15, 16]. Connectivity and/or ﬂow-amount are very important factors in applications to control and design of multimedia networks. In a multimedia network, a set S of some speciﬁed network nodes, such as the so-called mirror servers, may have functions of oﬀering the same services for users.