Abstract:
Since the pioneering work on multi-dimensional packing by Karp, Luby, and MarchettiSpaccamela [KLM] in 1984, stochastic matching problems in two and three dimensions have surfaced in the analysis of a surprising number of algorithms and systems, with applications in operations research, electrical engineering, and computer science. Thus, the related theory has provided an important analysis tool, one that, unfortunately, has yet to be applied by more than a handful of researchers. Of the several variants of stochastic matching that we will discuss, the following two have played fundamental roles. Let n plus points and n minus points (i.e., points labeled with +'s and \Gamma's) be chosen independently and uniformly at random in the unit square. Let M n denote a matching of the plus points to minus points and let (P \Gamma
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