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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Vydané v:	Journal of computer science and technology Ročník 23; číslo 5; s. 711 - 718
Hlavní autori:	Yang, Bing, Chen, Jing, Lu, En-Yue, Zheng, Si-Qing
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	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
Predmet:	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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Abstract	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.
AbstractList	TP3; 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) case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O(n3), a known greedy algorithm of time complexity O(n1.5 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. 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(n1.5) time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O(n3), a known greedy algorithm of time complexity O(n1.5 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. 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 [lfloor] 2 n + 1 4 - 1 2 [rfloor] 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 [lfloor] 2 n + 1 4 - 1 2 [rfloor] monotone subsequences in O(n super(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 super(3)), a known greedy algorithm of time complexity O(n super(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. 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.
Author	Zheng, Si-Qing Lu, En-Yue Yang, Bing Chen, Jing
AuthorAffiliation	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.;Department of Computer Science, University of Texas at Dallas, Richardson, TX 75083, U.S.A
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Author_xml	– sequence: 1 givenname: Bing surname: Yang fullname: Yang, Bing email: bingyang@cisco.com organization: Cisco Systems – sequence: 2 givenname: Jing surname: Chen fullname: Chen, Jing organization: Telecom. Engineering Program, University of Texas at Dallas – sequence: 3 givenname: En-Yue surname: Lu fullname: Lu, En-Yue organization: Department of Mathematics and Computer Science, Salisbury University – sequence: 4 givenname: Si-Qing surname: Zheng fullname: Zheng, Si-Qing organization: Telecom. Engineering Program, University of Texas at Dallas, Department of Computer Science, University of Texas at Dallas
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Publisher	Springer US 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
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Snippet	Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also,... TP3; Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications....
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SubjectTerms	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
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Title	Design and Performance Evaluation of Sequence Partition Algorithms
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