Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Programming pearls: algorithm design techniques
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Linear Time Algorithm for Finding All Maximal Scoring Subsequences
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
A BSP/CGM algorithm for finding all maximal contiguous subsequences of a sequence of numbers
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Scheduling links for heavy traffic on interfering routes in wireless mesh networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
A parallel algorithm for finding all successive minimal maximum subsequences
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Sequencing to minimize the maximum renewal cumulative cost
Operations Research Letters
A linear time algorithm for the k maximal sums problem
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Hi-index | 0.00 |
Let A be a sequence of n=0 real numbers. A subsequence of A is a sequence of contiguous elements of A. A maximum scoring subsequence of A is a subsequence with largest sum of its elements, which can be found in O(n) time by Kadane@?s dynamic programming algorithm. We consider in this paper two problems involving maximal scoring subsequences of a sequence. Both of these problems arise in the context of sequencing tasks to minimize the maximum renewal cumulative cost. The first one, which is called INSERTION IN A SEQUENCE WITH SCORES (ISS), consists in inserting a given real number x in A in such a way to minimize the sum of a maximum scoring subsequence of the resulting sequence, which can be easily done in O(n^2) time by successively applying Kadane@?s algorithm to compute the maximum scoring subsequence of the resulting sequence corresponding to each possible insertion position for x. We show in this paper that the ISS problem can be solved in linear time and space with a more specialized algorithm. The second problem we consider in this paper is the SORTING A SEQUENCE BY SCORES (SSS) one, stated as follows: find a permutation A^' of A that minimizes the sum of a maximum scoring subsequence. We show that the SSS problem is strongly NP-Hard and give a 2-approximation algorithm for it.