New Algorithms, Better Bounds, and a Novel Model for Online Stochastic Matching

Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popular model is the known I.I.D. model where different customer types arrive online from a known distribution. We develop algorithms with improved competitive ratios for some basic variants of this model with integral arrival rates, including (a) the case of general weighted edges, where we improve the best-known ratio of 0.667 due to Haeupler, Mirrokni and Zadimoghaddam to 0.705 and (b) the vertex-weighted case, where we improve the 0.7250 ratio of Jaillet and Lu to 0.7299. We also consider two extensions, one is known I.I.D. with non-integral arrival rate and stochastic rewards. The other is known I.I.D. b-matching with non-integral arrival rate and stochastic rewards. We present a simple non-adaptive algorithm which works well simultaneously on the two extensions.