Annals of Operations Research

, Volume 14, Issue 1, pp 105–123

The auction algorithm: A distributed relaxation method for the assignment problem

  • D. P. Bertsekas

DOI: 10.1007/BF02186476

Cite this article as:
Bertsekas, D.P. Ann Oper Res (1988) 14: 105. doi:10.1007/BF02186476


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.

Copyright information

© J.C. Baltzer A.G., Scientific Publishing Company 1988

Authors and Affiliations

  • D. P. Bertsekas
    • 1
  1. 1.Laboratory for Information and Decision SystemsMassachusetts Institute of TechnologyCambridge

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