Relay placement for fault tolerance in wireless networks in higher dimensions

Authors:
Abhishek Kashyap;Samir Khuller;Mark Shayman
Affiliations:
Electrical and Computer Engineering, University of Maryland, College Park, United States;Computer Science, University of Maryland, College Park, United States;Electrical and Computer Engineering, University of Maryland, College Park, United States
Venue:
Computational Geometry: Theory and Applications
Year:
2011

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Abstract

In this paper we consider the problem of adding the smallest number of additional (relay) nodes to a network of static nodes with limited communication range so that the induced communication graph is 2-connected (we consider both edge and vertex connectivity). The problem is NP-hard. We develop algorithms that find close to optimal solutions for both edge and vertex connectivity. We prove the algorithms have an approximation ratio of 2M for nodes distributed in a d-dimensional Euclidean space, where M is the maximum node degree of a Minimum Spanning Tree in d dimensions using Euclidean metrics. In addition, our methods extend with the same approximation guarantees to a generalization when the locations of relays are required to avoid certain polygonal regions (obstacles).