This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Parallel Pruning Technique for Highly Asymmetric Assignment Problems
June 2000 (vol. 11 no. 6)
pp. 550-558

Abstract—We introduce a new two-phase technique to solve highly asymmetric assignment problems. In the first phase, the assignment problem is decomposed into subproblems which are solved in parallel. The first phase is used to exclude certain suboptimal assignments from consideration in the second phase. In the second phase, the optimal assignment is finalized. We show that the two-phase algorithm can reduce the theoretical time bound for solving an $n \times k$ assignment problem ($ n < k$) by a factor of $\sqrt{\frac{k}{n}}$.

[1] M.M. Amini, “Vectorization of an Auction Algorithm for Linear Cost Assignment Problem,” Computers&Industrial Eng., vol. 26, no. 1, pp. 141–149, Jan. 1994.
[2] D.P. Bertsekas, “The Auction Algorithm for Assignment and Other Network Flow Problems: A Tutorial,” Interfaces, vol. 20, no. 4, pp. 133–149, July-Aug. 1990.
[3] D.P. Bertsekas, “Auction Algorithm for Network Flow Problems: A Tutorial Introduction,” Computational Optimization and Applications, vol. 1, pp. 277–297, 1992.
[4] D.P. Bertsekas, Linear Network Optimization: Algorithms and Codes. Cambridge, Mass.: MIT Press, 1991.
[5] D.P. Bertsekas and D.A. Castañon, “A Forward/Reverse Auction Algorithm for Asymmetric Assignment Problems,” Computational Optimization and Applications, vol. 1, pp. 277–297, 1992.
[6] D.P. Bertsekas and D.A. Castañon, “Parallel Synchronous and Asynchronous Implementations of the Auction Algorithm,” Parallel Computing, vol. 7,no. 6–7, pp. 707–732, Sept. 1991.
[7] D.P. Bertsekas and J. Eckstein, “Dual Coordinate Step Methods for Linear Network Flow Problems,” Math. Programming, series B, vol. 42, no. 2, pp. 203–243, 1988.
[8] D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation.Englewood Cliffs, N.J.: Prentice Hall International, 1989.
[9] L.L. Lasdon, Optimization Theory for Large Systems. New York: MacMillan Co., 1970.
[10] C.H. Papadimitriu and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity. Prentice Hall, 1987.
[11] J.B. Orlin and R.K. Ahuja, “New Scaling Algorithms for the Assignment and Minimum Mean Cycle Algorithms,” Math. Programming, vol. 54, pp. 41–56, 1992.
[12] B.L. Schwartz, A Computational, “Analysis of the Auction Algorithm,” European J. Operational Research, vol. 74, no. 1, pp. 161–169, Apr. 1994.
[13] J.M. Wein and S. Zenios, “Massively Parallel Auction Algorithms for the Assignment Problem,” Proc. Third Symp. Frontiers Massively Parallel Computation, J. JaJa, ed., IEEE CS Press, 1990.
[14] H.A. Zaki, “A Comparison of Two Algorithms for the Assignment Problem,” Computational Optimization and Applications, vol. 4, no. 1, pp. 23–45, 1995.

Index Terms:
Computational optimization, linear network flow, mathematical programming, parallel algorithm.
Citation:
Natalya Cohen, Jack Brassil, "A Parallel Pruning Technique for Highly Asymmetric Assignment Problems," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 6, pp. 550-558, June 2000, doi:10.1109/71.862206
Usage of this product signifies your acceptance of the Terms of Use.