A Simple 3-Approximation of Minimum Manhattan Networks
نویسندگان
چکیده
Given a set P of n points in the plane, a Manhattan network of P is a network that contains a rectilinear shortest path between every pair of points of P . Aminimum Manhattan network of P is a Manhattan network of minimum total length. It is unknown whether it is NP-hard to construct a minimum Manhattan network. The best approximations published so far are a combinatorial 3-approximation algorithm in time O(n log n), and an LP-based 2-approximation algorithm. We present a new combinatorial 3-approximation for this problem in time O(n log n). Both our algorithm and its analysis are considerably simpler than the prior 3-approximation.
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