On Very Large Scale Assignment Problems
In this paper we present computational testing results on very large scale random assignment problems. We consider a fully dense assignment problem with 2n nodes. Some conjectured or derived properties regarding fully dense assignment problems including the convergence of the optimal objective function value and the portion of nodes assigned with their kth best arc have been verified for networks up to n = 100,000 in size. Also we demonstrate the power of our approach in solving very large scale assignment problems by solving a one million node, one trillion arc random assignment problem.
KeywordsAssignment Problem Cost Distribution Short Path Tree Task Node Minimum Cost Flow Problem
Unable to display preview. Download preview PDF.
- M. Akgul . (1990), A Forest Primal-dual Algorithm for the Assignment Problem. Bilkent University, Ankara, Turkey, Research Report: IEOR-9014, 0 (0): 1–2.Google Scholar
- F. Avram and D. J. Bertsimas (1993), On a Characterization of the Minimum Assignment and Matching in the Independent Random Model. In The third Symposium in Integer Programming and Combinatorial Optimization, Enrice, Italy.Google Scholar
- D. P. Bertsekas (1990), “The Auction Algorithm for Assignment and other Network Flow Problems: A tutorial,” Interfaces 20 (4) 133–149.Google Scholar
- D. J. Bertsimas 1993, Personal Communication.Google Scholar
- R. M. Karp (1984), An Upper Bound on the Expected Cost of an Optimal Assignment Technical Report, Computer Science Division, University of California, Berkeley.Google Scholar
- Y. Lee and J. B. Orlin (1993), Quick Match: A Very Fast Algorithm for the Assignment Problem. Submitted to Mathematical Programming.Google Scholar
- M. Mezard and G. Parisi (1985), “Replicas and Optimization,” Journal de Physique Lettres 771–778.Google Scholar
- B. Olin (1992), Asymptotic Properties of Random Assignment Problems. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.Google Scholar
- P. M. Pardalos and K. G. Ramakrishnan (1993), On the Expected Optimal Value of Random Assignment Problems: Experimental Results and Open Questions.Google Scholar
- K. G. Ramakrishnan, N. K. Karmarkar, and A. P. Kamath (1992), An Approximate Dual Projective Algorithm for solving Assignment Problems. Technical Report 92–4, DIMACS.Google Scholar
- M. G. C. Resende and G. Veiga (1992), Computational Investigation of an Interior Point Linear Programming Algorithm for Minimum Cost Network Flows. Technical Report 92–4, Dimacs.Google Scholar