Greedy Construction of 2-Approximation Minimum Manhattan Network
نویسندگان
چکیده
Given a set T of n points in IR, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p, q ∈ T , in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network problem is to find a Manhattan network of the minimum length, i.e., the total length of the segments of the network is to be minimized. In this paper we present a 2-approximation algorithm with time complexity O(n log n), which improves the 2-approximation algorithm with time complexity O(n). Moreover, compared with other 2-approximation algorithms employing linear programming or dynamic programming technique, it was first discovered that only greedy strategy suffices to get 2-approximation network.
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