A linear-time algorithm for solving continuous maximin knapsack problems

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Abstract

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.

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    Two variants of the KSP exist in the literature: the continuous KSP and the binary KSP. The continuous KSP has been extensively studied by Tang (1988), Pang and Yu (1989), Brown (1991), Kuno, Konno, and Zemel (1991), Luss (1992) or Yamada and Futakawa (1997). A large variety of exact and approximate methods have been developed and adapted specifically for this problem.

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