An Integer Linear Program for Mixed-Weight Open Locating-Dominating Sets

Mixed-weight open locating-dominating sets (mixedweight OLD-sets) model systems that use sensors of multiple strengths to locate and detect problems in a network. Randomly-distributed wireless sensor networks, which often use sensors of different strengths, can be modeled by random geometric graphs. We build and study an Integer Linear Program to solve for mixed-weight OLD-sets and use greedy algorithms to generate mixed-weight OLD-set estimates in random geometric graphs. We also extend our previous results for mixed-weight OLD-sets in random graphs [6] to random geometric graphs by estimating the probabilistic upper bound for the size of the set.