Approximating the Generalized Minimum Manhattan Network Problem

作者：Das Aparna; Fleszar Krzysztof; Kobourov Stephen; Spoerhase Joachim^*; Veeramoni Sankar; Wolff Alexander

来源：Algorithmica, 2018, 80(4): 1170-1190.

DOI：10.1007/s00453-017-0298-0

• Approximation algorithms
• Computational geometry
• Minimum Manhattan Network

We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in . The goal is to find a minimum-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line segments whose total length equals the pair's Manhattan distance. This problem is a natural generalization of the extensively studied minimum Manhattan network problem (MMN) in which R consists of all possible pairs of terminals. Another important special case is the well-known rectilinear Steiner arborescence problem (RSA). As a generalization of these problems, GMMN is NP-hard. No approximation algorithms are known for general GMMN. We obtain an -approximation algorithm for GMMN. Our solution is based on a stabbing technique, a novel way of attacking Manhattan network problems. Some parts of our algorithm generalize to higher dimensions, yielding a simple -approximation algorithm for the problem in arbitrary fixed dimension d. As a corollary, we obtain an exponential improvement upon the previously best -ratio for MMN in d dimensions (ESA 2011). En route, we show that an existing -approximation algorithm for 2D-RSA generalizes to higher dimensions.

• 出版日期2018-4