Weighted Cache Location Problem with Identical Servers
This paper extends the well-known p -CLP with one server to p -CLP with m ≥ 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate...
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| Published in: | Journal of Applied Mathematics Vol. 2014; no. 2014; pp. 421 - 431-545 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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Cairo, Egypt
Hindawi Limiteds
01.01.2014
Hindawi Publishing Corporation John Wiley & Sons, Inc Wiley |
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| ISSN: | 1110-757X, 1687-0042 |
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| Abstract | This paper extends the well-known p -CLP with one server to p -CLP with m ≥ 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate ( p , m ) -CLP under CSOP to ( p , m ) -CSOP CLP and investigate that ( p , m ) -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m = 2 is the focus of this paper. We first devise an improved O ( p h 2 + n ) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O ( ( 4 / 9 ) p 2 n 2 ) time in the worst case for ( p , 2 ) -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m > 2 to obtain a worst-case O ( ( 4 / 9 ) ( n - m ) 2 ( ( m + p ) p / p - 1 ! ) ) -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. |
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| AbstractList | This paper extends the well-known p -CLP with one server to p -CLP with m> or =2 identical servers, denoted by (p,m) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate (p,m) -CLP under CSOP to (p,m) -CSOP CLP and investigate that (p,m) -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m=2 is the focus of this paper. We first devise an improved O(p super(h2) +n) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O((4/9) super(p2) super(n2) ) time in the worst case for (p,2) -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m>2 to obtain a worst-case O((4/9)(n-m super()2) ((m+p super()p) /p-1!)) -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. This paper extends the well-known p -CLP with one server to p -CLP with m ≥ 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate ( p , m ) -CLP under CSOP to ( p , m ) -CSOP CLP and investigate that ( p , m ) -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m = 2 is the focus of this paper. We first devise an improved O ( p h 2 + n ) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O ( ( 4 / 9 ) p 2 n 2 ) time in the worst case for ( p , 2 ) -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m > 2 to obtain a worst-case O ( ( 4 / 9 ) ( n - m ) 2 ( ( m + p ) p / p - 1 ! ) ) -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. This paper extends the well-known p -CLP with one server to p -CLP with m\ge 2 identical servers, denoted by (p,m) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate (p,m) -CLP under CSOP to (p,m) -CSOP CLP and investigate that (p,m) -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m=2 is the focus of this paper. We first devise an improved O(p{h}^{2}+n) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O((4/9){p}^{2}{n}^{2}) time in the worst case for (p,2) -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m>2 to obtain a worst-case O((4/9)(n-m{)}^{2}((m+p{)}^{p}/(p-1)!)) -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. This paper extends the well-known p-CLP with one server to p-CLP with m≥2 identical servers, denoted by (p,m)-CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate (p,m)-CLP under CSOP to (p,m)-CSOP CLP and investigate that (p,m)-CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m=2 is the focus of this paper. We first devise an improved O(ph2+n)-time parallel exact algorithm for p-CLP on a tree and then present a parallel exact algorithm with at most O((4/9)p2n2) time in the worst case for (p,2)-CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m>2 to obtain a worst-case O((4/9)(n-m)2((m+p)p/p-1!))-time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. This paper extends the well-known p -CLP with one server to p -CLP with m ≥ 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate ( p , m ) -CLP under CSOP to ( p , m ) -CSOP CLP and investigate that ( p , m ) -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m = 2 is the focus of this paper. We first devise an improved O ( p h 2 + n ) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O ( ( 4 / 9 ) p 2 n 2 ) time in the worst case for ( p , 2 ) -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m > 2 to obtain a worst-case O ( ( 4 / 9 ) ( n - m ) 2 ( ( m + p ) p / p - 1 ! ) ) -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. This paper extends the well-known p -CLP with one server to p -CLP with m ...5; 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate ( p , m ) -CLP under CSOP to ( p , m ) -CSOP CLP and investigate that ( p , m ) -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m = 2 is the focus of this paper. We first devise an improved O ( p [superscript] h 2 [/superscript] + n ) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O ( ( 4 / 9 ) [superscript] p 2 [/superscript] [superscript] n 2 [/superscript] ) time in the worst case for ( p , 2 ) -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m > 2 to obtain a worst-case O ( ( 4 / 9 ) ( n - m [superscript] ) 2 [/superscript] ( ( m + p [superscript] ) p [/superscript] / p - 1 ! ) ) -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms. |
| Author | Ding, Wei Wang, Hongfa |
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| Copyright | Copyright © 2014 Hongfa Wang and Wei Ding. Copyright © 2014 Hongfa Wang and Wei Ding. Hongfa Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright 2014 Hindawi Publishing Corporation |
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| References_xml | – volume: 19 start-page: 510 year: 2004 end-page: 514 ident: 17 article-title: Web proxy location problem in the tree networks – volume: 35 start-page: 170 issue: 6 year: 1997 end-page: 178 ident: 1 article-title: World wide web caching: the application-level view of the internet – reference: Yeager N. McGrath R. Web Server Technology: The Advanced Guide for World Wide Web Information Providers 1996 San Francisco, Calif, USA Morgan Kaufmann Publishers – reference: Chankhunthod A. Danzig P. Neerdaels C. Schwartz M. Worrell K. A hierarchical internet object cache Proceedings of the Annual Conference on USENIX Annual Technical Conference (ATEC '96) 1996 Berkeley, Calif, USA USENIX Association 13 – volume: 26 start-page: 293 issue: 4 year: 1996 end-page: 305 ident: 7 article-title: Removal policies in network caches for World-Wide Web documents – volume: 27 start-page: 165 issue: 2 year: 1994 end-page: 173 ident: 3 article-title: A caching relay for the World Wide Web – volume: 37 start-page: 539 issue: 3 year: 1979 end-page: 560 ident: 14 article-title: An Algorithmic Approach to Network Location Problems. II: the -Medians – reference: Ding W. Xue G. 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On the optimal placement of Web proxies in the Internet: linear topology Proceedings of the IFIP TC-6 8th International Conference on High Performance Networking (HPN '98) September 1998 Vienna, Austria 485 495 – volume: 45 start-page: 109 issue: 31 year: 2009 end-page: 110 ident: 21 article-title: Delay-constrained Web proxy problem in Internet – reference: Malpani R. Lorch J. Berger D. Making world wide web caching servers cooperate Proceedings of the 4th International World-Wide Web Conference December 1995 Boston, Mass, USA 107 117 – volume: 19 start-page: 59 issue: 2 year: 1996 end-page: 64 ident: 15 article-title: An O( ) algorithm for the p-median and related problems on tree graphs – volume: 8 start-page: 568 issue: 5 year: 2000 end-page: 582 ident: 11 article-title: The cache location problem – reference: Li B. Golin M. J. Italiano G. F. Deng X. Sohraby K. On the optimal placement of web proxies in the Internet Proceedings of the 18th Annual Joint Conference of the IEEE Computer and Communications Societie (INFOCOM '99) March 1999 New York, NY, USA 1282 1290 2-s2.0-0032661528 – reference: Bondy J. A. Murty U. S. R. Graph Theory with Application 1976 London, UK Macmillan MR0411988 – volume: 46 start-page: 378 issue: 4 year: 2003 end-page: 390 ident: 20 article-title: Placement of Web-server proxies with consideration of read and update operations on the Internet – volume: 1 start-page: 269 year: 1959 end-page: 271 ident: 23 article-title: A note on two problems in connexion with graphs – reference: Heddaya A. Mirdad S. WebWave: globally load balanced fully distributed caching of hot published documents Proceedings of the 17th International Conference on Distributed Computing Systems (ICDCS '97) May 1997 Baltimore, Md, USA 160 168 2-s2.0-0030646557 – reference: Du D. Placement of read-write Web proxies in the Internet Proceedings of the The 21st International Conference on Distributed Computing Systems (ICDCS '01) April 2001 Phoenix, Ariz, USA 687 687 – volume: 2013 year: 2013 end-page: 11 ident: 24 article-title: On the 2-MRS problem in a tree with unreliable edges – volume: 12 start-page: 327 issue: 4 year: 2006 end-page: 336 ident: 18 article-title: The web proxy location problem in general tree of rings networks – volume: 19 start-page: 510 year: 2004 ident: 6 publication-title: Applied Mathematics A: Journal of Chinese Universities – ident: 9 doi: 10.1007/BF01386390 – ident: 17 doi: 10.1093/comjnl/46.4.378 – year: 1976 ident: 3 – volume: 23 start-page: 239 issue: 4 year: 1993 ident: 8 publication-title: ACM SIGCOMM Computer Communication Review doi: 10.1145/167954.166260 – ident: 2 doi: 10.1109/35.587725 – ident: 11 doi: 10.1155/2013/743908 – year: 1996 ident: 27 – volume: 28 start-page: 241 issue: 4 year: 1998 ident: 7 publication-title: Computer Communication Review doi: 10.1145/285243.285286 – volume: 26 start-page: 293 issue: 4 year: 1996 ident: 1 publication-title: ACM SIGCOMM Computer Communication Review doi: 10.1145/248157.248182 – volume: 45 start-page: 109 issue: 31 year: 2009 ident: 23 publication-title: Computer Engineering and Applications – volume: 30 start-page: 195 issue: 1–7 year: 1998 ident: 20 publication-title: Computer Networks and ISDN Systems – ident: 10 doi: 10.1007/978-3-642-22616-8_9 – ident: 25 doi: 10.1016/0167-6377(96)00021-1 – ident: 26 doi: 10.1016/S0167-6377(00)00041-9 – ident: 14 doi: 10.1016/0169-7552(94)90130-9 – ident: 18 doi: 10.1137/0137041 – ident: 19 doi: 10.1109/90.879344 – ident: 5 doi: 10.1007/s10878-006-9002-z |
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| Snippet | This paper extends the well-known p -CLP with one server to p -CLP with m ≥ 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server... This paper extends the well-known p -CLP with one server to p -CLP with m ≥ 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server... This paper extends the well-known p -CLP with one server to p -CLP with m ...5; 2 identical servers, denoted by ( p , m ) -CLP. We propose the closest server... This paper extends the well-known p -CLP with one server to p -CLP with m> or =2 identical servers, denoted by (p,m) -CLP. We propose the closest server... This paper extends the well-known p -CLP with one server to p -CLP with m\ge 2 identical servers, denoted by (p,m) -CLP. We propose the closest server... This paper extends the well-known p-CLP with one server to p-CLP with m≥2 identical servers, denoted by (p,m)-CLP. We propose the closest server orienting... |
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| StartPage | 421 |
| SubjectTerms | Algorithms Dynamic programming Equivalence Heuristic Networks Production scheduling Running Series (mathematics) Servers Servers (computers) Trees |
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| Title | Weighted Cache Location Problem with Identical Servers |
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| Volume | 2014 |
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