1. GREEDY CONSTRUCTION OF 2-APPROXIMATE MINIMUM MANHATTAN NETWORKS.
- Author
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GUO, ZEYU, SUN, HE, ZHU, HONG, Hong, Seok-Hee, and Nagamochi, Hiroshi
- Subjects
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APPROXIMATION theory , *ALGORITHMS , *GRAPH theory , *PATHS & cycles in graph theory , *GRAPH connectivity , *LINEAR programming , *DYNAMIC programming , *MATHEMATICAL analysis - Abstract
Given a set T of n points in ℝ2, a Manhattan network on T is a graph G = (V,E) with the property that all the edges in E are vertical or horizontal line segments connecting points in V ⊇ T and for all p, q ∈ T, the graph contains a path having the length exactly L1 distance between p and q. The Minimum Manhattan Network problem is to find a Manhattan network of minimum length, i.e. minimizing the total length of the line segments of the network. In this paper we present a 2-approximation algorithm with time complexity O(n log n), which improves over a recent combinatorial 2-approximation algorithm with running time O(n2). Moreover, compared with other 2-approximation algorithms using linear programming or dynamic programming techniques, we show that a greedy strategy suffices to obtain a 2-approximation algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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