Design and Performance Evaluation of Sequence Partition Algorithms

• Published in: Journal of computer science and technology Vol. 23; no. 5; pp. 711 - 718
• Main Authors: Yang, Bing, Chen, Jing, Lu, En-Yue, Zheng, Si-Qing
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.09.2008; Springer Nature B.V; Department of Computer Science, University of Texas at Dallas, Richardson, TX 75083, U.S.A; Cisco Systems, 2200 East President George Bush Highway, Richardson, TX 75082, U.S.A.%Teleeom. Engineering Program, University of Texas at Dallas, Richardson, TX 75083, U.S.A.%Department of Mathematics and Computer Science, Salisbury University, Salisbury, MD 21801, U.S.A.%Teleeom. Engineering Program, University of Texas at Dallas, Richardson, TX 75083, U.S.A
• Subjects: Algorithms; Approximation; Artificial Intelligence; Complexity; Computation; Computer Science; Data Structures and Information Theory; Greedy algorithms; Information Systems Applications (incl.Internet); Mathematical analysis; Mathematical models; Optimization; Performance evaluation; Regular Paper; Software Engineering; Studies; Theory of Computation; Upper bounds; complexity; permutation algorithm; approximation; NP-complete; monotone subsequence
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/s11390-008-9183-2

Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual solution optimality for realistic instances of an NP-hard problem is a factor in selecting algorithms in practice. We consider the problem of partitioning a sequence of n distinct numbers into minimum number of monotone (increasing or decreasing) subsequences. This problem is NP-hard and the number of monotone subsequences can reach in the worst case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no more than monotone subsequences in O ( n 1.5 ) time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O ( n 3 ), a known greedy algorithm of time complexity O ( n 1.5 log n ), and our new modified Yehuda-Fogel algorithm. Our results show that the solutions computed by the greedy algorithm and the modified Yehuda-Fogel algorithm are close to that computed by the approximation algorithm even though the theoretical worst-case error bounds of these two algorithms are not proved to be within a constant time of the optimal solution. Our study indicates that for practical use the greedy algorithm and the modified Yehuda-Fogel algorithm can be good choices if the running time is a major concern.