TY - GEN

T1 - Characterization and algorithms for greedily solvable transportation problems

AU - Shamir, Ron

AU - Dietrich, Brenda

N1 - Funding Information:
* DIMACS Center and Tel Aviv University, Current address: DIMACS Center, Rutgers University, Box 1179, Piscataway NJ 08855 1 I79 # IBM Watson Research Center, Box 218, Yorktown Heights NY, 10598 + Supported in part by Allon Fellowship

PY - 1990/1/1

Y1 - 1990/1/1

N2 - We study transportation problems in which shipping between certain sources and destinations is disallowed. Given such a problem we seek a permutation of the decision variables which, when used by the greedy algorithm, which maximizes each variable in turn according to the order prescribed by the permutation, provides an optimal solution for every feasible supply and demand vectors. We give a necessary and sufficient condition under which a permutation satisfies that requirement, and devise an efficient algorithm which constructs such a permutation or determines that none exist. Our characterization and the algorithm are based on Hoffman's notion of Monge sequences, as denned for the special case when no shippings are disallowed, and on an antimatroid interpretation of this notion. The running time of our algorithm is better than that of the best known algorithms for solving the transportation problem, both for sparse and for dense problems. Having constructed such a permutation, a solution of any problem with that cost matrix can be obtained in linear time.

AB - We study transportation problems in which shipping between certain sources and destinations is disallowed. Given such a problem we seek a permutation of the decision variables which, when used by the greedy algorithm, which maximizes each variable in turn according to the order prescribed by the permutation, provides an optimal solution for every feasible supply and demand vectors. We give a necessary and sufficient condition under which a permutation satisfies that requirement, and devise an efficient algorithm which constructs such a permutation or determines that none exist. Our characterization and the algorithm are based on Hoffman's notion of Monge sequences, as denned for the special case when no shippings are disallowed, and on an antimatroid interpretation of this notion. The running time of our algorithm is better than that of the best known algorithms for solving the transportation problem, both for sparse and for dense problems. Having constructed such a permutation, a solution of any problem with that cost matrix can be obtained in linear time.

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AN - SCOPUS:84916293685

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 358

EP - 366

BT - Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990

PB - Association for Computing Machinery

T2 - 1st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1990

Y2 - 22 January 1990 through 24 January 1990

ER -