Complexity of min-max subsequence problems

Authors:
Wil Michiels;Jan Korst
Affiliations:
Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands and Technische Universiteit Eindhoven, Department of Mathematics and Computing Science, Eindhoven, The Netherla ...;Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands
Venue:
Information Processing Letters
Year:
2003

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Abstract

We determine the computational complexity of the problem of ordering a set of n numbers, either into a sequence or a cycle, such that the maximum sum of any k successive numbers is minimal. Both problems are easy for k = 2 and strongly NP-hard for any k ≥ 3. However, the two problems allow a polynomial-time approximation scheme that is linear in n.