Titlebook: Algorithms and Data Structures; 10th International W Frank Dehne,J?rg-Rüdiger Sack,Norbert Zeh Conference proceedings 2007 Springer-Verlag

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A Near Linear Time Approximation Scheme for Steiner Tree Among Obstacles in the Plane.), where . denotes the number of terminals plus obstacle vertices. To this end, we show how a planar spanner of size .(. log.) can be constructed that contains a (1?+?.)-approximation of the optimal tree. Then one can find an approximately optimal Steiner tree in the spanner using the algorithm of

ALIEN

A Pseudopolynomial Time ,(log,)-Approximation Algorithm for Art Gallery Problemstime polynomial in ., the number of walls of the art gallery and the spread ., which is defined as the ratio between the longest and shortest pairwise distances. Our algorithm is pseudopolynomial in the sense that it is polynomial in the spread . as opposed to polylogarithmic in the spread ., which

積云

Optimization for First Order Delaunay Triangulations-adjacent or vertex-adjacent triangles instead of only to single triangles. We give efficient algorithms to optimize certain measures, whereas other measures are shown to be NP-hard. For two of the NP-hard maximization problems we provide for any constant .>?0, factor (1???.) approximation algorithm

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Kinderszenen: Irrationales in der Musik,e that supports orthogonal range reporting queries in .(log.?+?.log..) time, where . is the size of the answer. Our data structure also supports emptiness and one-reporting queries in .(log.) time and thus achieves optimal time and space for this type of queries. In the case of integer point coordin