Inexpensive d-dimensional matchings

Authors:
Bae-Shi Huang;Ljubomir Perković;Eric Schmutz
Affiliations:
MCS Department, Drexel University, 3141 Chestnut Street, Philadelphia, PA;MCS Department, Drexel University, 3141 Chestnut Street, Philadelphia, PA;MCS Department, Drexel University, 3141 Chestnut Street, Philadelphia, PA
Venue:
Random Structures & Algorithms
Year:
2002

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Abstract

Suppose that independent U(0, 1) weights are assigned to the (3/16)n2 edges of the complete d-partite graph with n vertices in each of the d maximal independent sets. Then the expected weight of the minimum-weight perfect d-dimensional matching is at least 3/16n1-(2/d). We describe a randomized algorithm that finds a perfect d-dimensional matching whose expected weight is at most 5d3n1-(2/d)+ d15 for all d ≥ 3 and n ≥ 1.