A linear-time algorithm for solving continuous maximin knapsack problems

This paper introduces a special class of mathematical programming problem which maximizes the minimal value of a set of linear functions subject to a single linear constraint and upper bounding constraint on each variable. An O(n) algorithm for solving this problem is described by exploiting its special structure.

[1]  Marc E. Posner,et al.  Linear max-min programming , 1981, Math. Program..

[2]  H. Greenberg,et al.  A Branch Search Algorithm for the Knapsack Problem , 1970 .

[3]  H. Konno,et al.  A mofified gub algorithm for solving linear minimax problems , 1989 .

[4]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

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

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

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

[8]  Prabhakant Sinha,et al.  The Multiple-Choice Knapsack Problem , 1979, Oper. Res..

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

[10]  Seymour Kaplan Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation , 1974, Oper. Res..

[11]  Eitan Zemel,et al.  The Linear Multiple Choice Knapsack Problem , 1980, Oper. Res..

[12]  Nimrod Megiddo,et al.  Applying parallel computation algorithms in the design of serial algorithms , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[13]  Horst A. Eiselt Continuous maximin knapsack problems with GLB constraints , 1986, Math. Program..

[14]  R. Ahuja Minimax linear programming problem , 1985 .

[15]  Nimrod Megiddo Combinatorial Optimization with Rational Objective Functions , 1979, Math. Oper. Res..