Programming pearls: algorithm design techniques
Communications of the ACM
Journal of Computer and System Sciences - Computational biology 2002
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
An optimal algorithm for maximum-sum segment and its application in bioinformatics
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
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In this paper, we propose to study the famous maximum sum segment problem on a sequence consisting of n uncertain numbers, where each number is given as an interval characterizing its possible value. Given two integers L and U , a segment of length between L and U is called a potential maximum sum segment if there exists a possible assignment of the uncertain numbers such that, under the assignment, the segment has maximum sum over all segments of length between L and U . We define the maximum sum segment with uncertainty problem, which consists of two sub-problems: (1) reporting all potential maximum sum segments; (2) counting the total number of those segments. For L =1 and U =n , we propose an O (n +K )-time algorithm and an O (n )-time algorithm, respectively, where K is the number of potential maximum sum segments. For general L and U , we give an O (n (U −L ))-time algorithm for either problem.