Maximizing Submodular Set Function with Connectivity Constraint: Theory and Application to Networks

Abstract

In this paper, we investigate the wireless network deployment problem, which seeks the best deployment of a given limited number of wireless routers. We find that many goals for network deployment, such as maximizing the number of covered users, the size of the coverage area, or the total throughput of the network, can be modeled with a submodular set function. Specifically, given a set of routers, the goal is to find a set of locations S, each of which is equipped with a router, such that S maximizes a predefined submodular set function. However, this deployment problem is more difficult than the traditional maximum submodular set function problem, e.g., the maximum coverage problem, because it requires all the deployed routers to form a connected network. In addition, deploying a router in different locations might consume different costs. To address these challenges, this paper introduces two approximation algorithms, one for homogeneous deployment cost scenarios and the other for heterogeneous deployment cost scenarios. Our simulations, using synthetic data and real traces of census in Taipei, Taiwan, show that the proposed algorithms achieve better performances than other heuristics.