Online Primal Dual Meets Online Matching with Stochastic Rewards: Configuration LP to the Rescue

Abstract

<p>Mehta and Panigrahi (FOCS 2012, IEEE, Piscataway, NJ, 2012, pp. 728-737) introduce the problem of online matching with stochastic rewards, where edges are associated with success probabilities and a match succeeds with the probability of the corresponding edge. It is one of the few online matching problems that have defied the randomized online primal dual framework by Devanur, Jain, and Kleinberg (SODA 2013, SIAM, Philadelphia, 2013, pp. 101-107) thus far. This paper unlocks the power of randomized online primal dual in online matching with stochastic rewards by employing the configuration linear program rather than the standard matching linear program used in previous works. Our main result is a 0.572 competitive algorithm for the case of vanishing and unequal probabilities, improving the best previous bound of 0.534 by Mehta, Waggoner, and Zadimoghaddam (SODA 2015, SIAM, Philadelphia, 2015, pp. 1388-1404) and, in fact, is even better than the best previous bound of 0.567 by Mehta and Panigrahi (FOCS 2012, IEEE, Piscataway, NJ, 2012, pp. 728-737) for the more restricted case of vanishing and equal probabilities. For vanishing and equal probabilities, we get a better competitive ratio of 0.576. Our results further generalize to the vertex-weighted case due to the intrinsic robustness of the randomized online primal dual analysis.</p>