A faster polynomial algorithm for the unbalanced Hitchcock transportation problem

We present a new algorithm for the Hitchcock transportation problem. On instances with n sources and k sinks, our algorithm has a worst-case running time of O(nk^2(logn+klogk)). It closes a gap between algorithms with running time linear in n but exponential in k and a polynomial-time algorithm with running time O(nk^2log^2n).

[1]  Egon Balas,et al.  An Algorithm for Large Zero-One Knapsack Problems , 1980, Oper. Res..

[2]  Ulrich Brenner,et al.  Faster and better global placement by a new transportation algorithm , 2005, Proceedings. 42nd Design Automation Conference, 2005..

[3]  Andrew V. Goldberg,et al.  Finding Minimum-Cost Circulations by Successive Approximation , 1990, Math. Oper. Res..

[4]  Takeshi Tokuyama,et al.  Geometric algorithms for a minimum cost assignment problem , 1991, SCG '91.

[5]  Jens Vygen,et al.  The Book Review Column1 , 2020, SIGACT News.

[6]  Gerhard J. Woeginger,et al.  A linear-time algorithm for the bottleneck transportation problem with a fixed number of sources , 1999, Oper. Res. Lett..

[7]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[8]  Donald B. Johnson,et al.  Selecting the Kth element in X + Y and X_1 + X_2 + ... + X_m , 1978, SIAM J. Comput..

[9]  Eitan Zemel,et al.  An O(n) Algorithm for the Linear Multiple Choice Knapsack Problem and Related Problems , 1984, Inf. Process. Lett..

[10]  Martin Dyer,et al.  AN O(n) ALGORITHM FOR THE MULTIPLE-CHOICE , 2007 .

[11]  Takeshi Tokuyama,et al.  Efficient algorithms for the Hitchcock transportation problem , 1992, SODA '92.

[12]  Robert E. Tarjan,et al.  Improved Algorithms for Bipartite Network Flow , 1994, SIAM J. Comput..

[13]  Peter Kleinschmidt,et al.  A strongly polynomial algorithm for the transportation problem , 1995, Math. Program..

[14]  Manuel Blum,et al.  Time Bounds for Selection , 1973, J. Comput. Syst. Sci..

[15]  James B. Orlin.  A Faster Strongly Polynomial Minimum Cost Flow Algorithm , 1993, Oper. Res..

[16]  Donald L. Adolphson,et al.  A Linear Time Algorithm for a 2 × n Transportation Problem , 1977, SIAM J. Comput..

[17]  Jens Vygen,et al.  Geometric quadrisection in linear time, with application to VLSI placement , 2005, Discret. Optim..

[18]  Nimrod Megiddo,et al.  Linear time algorithms for some separable quadratic programming problems , 1993, Oper. Res. Lett..

[19]  M. Klein.  A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems , 1966 .