The auction algorithm: A distributed relaxation method for the assignment problem
 D. P. Bertsekas
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We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. The algorithm can also be interpreted as a Jacobi — like relaxation method for solving a dual problem. Its (sequential) worst — case complexity, for a particular implementation that uses scaling, is O(NAlog(NC)), where N is the number of persons, A is the number of pairs of persons and objects that can be assigned to each other, and C is the maximum absolute object value. Computational results show that, for large problems, the algorithm is competitive with existing methods even without the benefit of parallelism. When executed on a parallel machine, the algorithm exhibits substantial speedup.
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 Title
 The auction algorithm: A distributed relaxation method for the assignment problem
 Journal

Annals of Operations Research
Volume 14, Issue 1 , pp 105123
 Cover Date
 19881201
 DOI
 10.1007/BF02186476
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Baltzer Science Publishers, Baarn/Kluwer Academic Publishers
 Additional Links
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 Industry Sectors
 Authors

 D. P. Bertsekas ^{(1)}
 Author Affiliations

 1. Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, Mass.