Approximating Minimum Manhattan Networks
- Joachim GudmundssonAffiliated withDept. of Computer Science, Lund University
- , Christos LevcopoulosAffiliated withDept. of Computer Science, Lund University
- , Giri NarasimhanAffiliated withDept. of Mathematical Sciences, The Univ. of Memphis
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 ∪ S′. A Manhattan network can also be thought of as a 1-spanner (for the L 1-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(n 3)-time algorithm with approximation factor four, and an O(n log n)-time algorithm with approximation factor eight.
- Approximating Minimum Manhattan Networks
- Book Title
- Randomization, Approximation, and Combinatorial Optimization. Algorithms and Techniques
- Book Subtitle
- Third International Workshop on Randomization and Approximation Techniques in Computer Science, and Second International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, RANDOM-APPROX’99, Berkeley, CA, USA, August 8-11, 1999.
- pp 28-38
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Editor Affiliations
- 4. Department of Industrial Engineering and Operations Research and Walter A. Haas School of Business, University of California
- 5. Institute for Computer Science, University of Kiel
- 6. Centre Universitaire d’Informatique
- 7. Computer Science Division, University of California
- Author Affiliations
- 8. Dept. of Computer Science, Lund University, Box 118, 221 00, Lund, Sweden
- 9. Dept. of Mathematical Sciences, The Univ. of Memphis, Memphis, TN, 38152, USA
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