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arXiv · 2403.11811

A Simple 2-Approximation Algorithm For Minimum Manhattan Network Problem

Md. Musfiqur Rahman Sanim·Safrunnesa Saira·Fatin Faiaz Ahsan·Rajon Bardhan·S. M. Ferdous
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Abstract

Given a n points in two dimensional space, a Manhattan Network G is a network that connects all n points with either horizontal or vertical edges, with the property that for any two point in G should be connected by a Manhattan path and distance between this two points is equal to Manhattan Distance. The Minimum Manhattan Network problem is to find a Manhattan network with minimum network length, i.e., summation of all line segment in network should be minimize. In this paper, we proposed a 2-approximation algorithm with time complexity O(|E|lgN) where |E| is the number of edges and N is the number of nodes. Using randomly generated datasets, we compare our result with the optimal one.

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Md. Musfiqur Rahman Sanim, Safrunnesa Saira, Fatin Faiaz Ahsan, Rajon Bardhan, S. M. Ferdous. 2024-03-18. A Simple 2-Approximation Algorithm For Minimum Manhattan Network Problem. https://arxiv.org/abs/2403.11811

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