Design and Performance Evaluation of Sequence Partition Algorithms

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 se...

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Vydáno v:Journal of computer science and technology Ročník 23; číslo 5; s. 711 - 718
Hlavní autoři: Yang, Bing, Chen, Jing, Lu, En-Yue, Zheng, Si-Qing
Médium: Journal Article
Jazyk:angličtina
Vydáno: 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
Témata:
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
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Shrnutí: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.
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ISSN:1000-9000
1860-4749
DOI:10.1007/s11390-008-9183-2