A Fast Mixed Integer Programming Formulation for the Maximum Set Covers Problem in Wireless Sensor Networks

Abstract

In a wireless sensor network (WSNET), the target coverage (TC) problem is to schedule the activity of each sensor such that each target is monitored by some sensor at every moment and the network lifetime is maximized. A possible approach to deal with the TC problem is to organize all the sensors into a group of non-disjoint sets such that each set can completely monitor all the targets within a certain time interval and only one set is active at any time instant. This approach is known as the maximum set covers (MSC) problem, which has been proven to be NP-complete. In this paper, the MSC problem is studied. There has existed a mixed integer programming formulation (MIPF) for the MSC problem, named as MIPF-for-MSC, which can find its optimal solution. However, the execution time of MIPF-for-MSC is heavy. In this paper, we design a preprocessing technique and a new inequality to speed up the execution of MIPF-for-MSC. Computer simulations show that compared with the original MIPF-for-MSC, our preprocessing technique and new inequality can reduce the execution time significantly.