Bidirected minimum Manhattan network problem

TL;DR

This paper introduces a polynomial factor 2 approximation algorithm for constructing the minimum-length directed Manhattan network connecting all terminal pairs in the plane, optimizing network design for directed paths.

Contribution

It presents the first polynomial factor 2 approximation algorithm for the bidirected minimum Manhattan network problem, improving upon previous approaches.

Findings

Algorithm achieves a factor 2 approximation ratio

Efficient polynomial-time solution for the problem

Provides theoretical guarantees for network length

Abstract

In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, we need to construct a network N(T) of minimum total length with the property that the edges of N(T) are axis-parallel and oriented in a such a way that every ordered pair of terminals is connected in N(T) by a directed Manhattan path. In this paper, we present a polynomial factor 2 approximation algorithm for the bidirected minimum Manhattan network problem.