Nordic Journal of Computing Bibliography

Joachim Gudmundsson, Christos Levcopoulos, and Giri Narasimhan. Approximating a Minimum Manhattan Network. Nordic Journal of Computing, 8(2):219-232, Summer 2001.

Given a set S of n points in the plane, we define a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G=(V,E), where the vertex set V corresponds to points from S and a set of Steiner points S', and the edges in E correspond to horizontal or vertical line segments connecting points in S U S'. A Manhattan network can also be thought of as a 1-spanner (for the L1-metric) for the points in S.

Let R be an algorithm that produces a rectangulation of a staircase polygon in time R(n) of weight at most r times the optimal. We design an O(n\log n + R(n)) time algorithm which, given a set S of n points in the plane, produces a Manhattan network on S with total weight at most 4r times that of a minimum Manhattan network. Using known rectangulation algorithms, this gives us an O(n3)-time algorithm with approximation factor four, and an O(n \log n)-time algorithm with approximation factor eight.

Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling

Additional Key Words and Phrases: computational geometry, approximation algorithms, spanners

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