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|All Authors / Contributors:||
Gil Kalai; Larry Stockmeyer
|Notes:||"November 1, 1991."|
|Description:||13 pages ; 28 cm.|
|Series Title:||International Business Machines Corporation.; Research Division.; Research report|
|Responsibility:||Gil Kalai, Larry Stockmeyer.|
Abstract: "As defined by Awerbuch and Peleg, an m-regional matching for a graph G = (V, E) is a family of sets R(u), W(u) [subset of] V for u [member of] V, such that if the distance between vertices v and w is at most m then R(v) intersects W(w). We define a probabilistic generalization of a regional matching, and prove a lower bound on the complexity of any m-regional matching for the hypercube graph, where the complexity is measured in terms of the maximum size and radius of the sets R(u) and W(u). We use this lower bound to give a lower bound on the communication complexity of any probabilistic algorithm for the problem of on-line tracking of a mobile user on the hypercube. In the course of proving the lower bound on the complexity of regional matchings, we consider a generalization of the vertex isoperimetric problem on the cube."
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