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

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426 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)105-123
Number of pages19
JournalAnnals of Operations Research
Issue number1
StatePublished - Dec 1988
Externally publishedYes

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Management Science and Operations Research


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