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The Random Graph Threshold for korientiability and a Fast Algorithm for Optimal MultipleChoice Allocation
, 2007
"... We investigate a linear time greedy algorithm for the following load balancing problem: Assign m balls to n bins such that the maximum occupancy is minimized. Each ball can be placed into one of two randomly choosen bins. This problem is closely related to the problem of orienting the edges of an un ..."
Abstract

Cited by 12 (2 self)
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We investigate a linear time greedy algorithm for the following load balancing problem: Assign m balls to n bins such that the maximum occupancy is minimized. Each ball can be placed into one of two randomly choosen bins. This problem is closely related to the problem of orienting the edges of an undirected graph to obtain a directed graph with minimum indegree. Using differential equation methods, we derive thresholds for the solution quality achieved by our algorithm. Since these thresholds coincide with lower bounds for the achievable solution quality, this proves the optimality of our algorithm (as n → ∞, in a probabilistic sense) and establishes the thresholds for korientability of random graphs. This proves an assertion of Karp and Saks.