2018/08/09 by Ashlagi, Itai, Burq, Maximilien, Dutta, Chinmoy +3 · 1 citation
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1808.03526
We study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and the planner's goal is to maximize the total value over a finite time horizon. First we study the case in which vertices arrive in an adversarial order. We provide a randomized 0.25-competitive algorithm building on a result by Feldman et al. (2009) and Lehman et al. (2006). We extend the model to the case in which departure times are drawn independently from a distribution with non-decreasing hazard rate, for which we establish a 1/8-competitive algorithm. When the arrival order is chosen uniformly at random, we show that a batching algorithm, which computes a maximum-weighted matching every (d+1) periods, is 0.279-competitive.