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  1. NTU Theses and Dissertations Repository
  2. 電機資訊學院
  3. 資訊工程學系
請用此 Handle URI 來引用此文件: http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70275
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DC 欄位值語言
dc.contributor.advisor陳健輝
dc.contributor.authorKeng-Chien Changen
dc.contributor.author張耿健zh_TW
dc.date.accessioned2021-06-17T04:25:07Z-
dc.date.available2020-08-16
dc.date.copyright2018-08-16
dc.date.issued2018
dc.date.submitted2018-08-15
dc.identifier.citation[1] H. A. Harutyunyan and C. Jimborean, “New heuristic for message broadcasting in networks,” Proceedings of the 28th IEEE International Conference on Advanced Information Networking and Applications, pp. 517–524, 2014.
[2] H. Harutyunyan, A. Liestman, J. Peters, and D. Richards, “Broadcasting and gossiping, in: Handbook of graph theory, second edition,” Chapman and Hall/CRC, pp. 1477–1494, 2013.
[3] H. Harutyunyan and A. Liestman, “Improved upper and lower bounds for kbroadcasting,”Networks, vol. 37, pp. 94–101, 2001.
[4] H. Harutyunyan and A. Liestman, “k-broadcasting in trees,” Networks, vol. 38,pp. 163–168, 2001.
[5] H. Harutyunyan, A. Liestman, K. Makino, and T. Shermer, “Nonadaptive broadcastingin trees,” Networks, vol. 57, pp. 157–168, 2011.
[6] H. Harutyunyan, A. Liestman, and B. Shao, “A linear algorithm for finding the kbroadcastcenter of a tree,” Networks, vol. 53, pp. 287–292, 2009.
[7] H. Harutyunyan and B. Shao, “An efficient heuristic for broadcasting in networks,”J. Parallel Distrib. Comput., vol. 66, no. 1, pp. 68–76, 2006.
[8] P. J. Slater, E. J. Cockayne, and S. T. Hedetniemi, “Information of dissemination in trees.,” SIAM J. Comput., vol. 10, no. 4, p. 692–701, 1981.
[9] P. J. Slater, E. J. Cockayne, and S. T. Hedetniemi, “Information dissemination in trees with nonuniform edge transmission times,” IEEE Trans. Comput., vol. 40, no.10, pp. 1174–1177, 1991.
[10] G. Kortsarz and D. Peleg, “Approximation algorithms for minimum time broadcast.,”SIAM J. Discrete Math, vol. 8, pp. 401–427, 1995.
[11] M.Elkin and G. Kortsarz, “Sublogarithmic approximation for telephone multicast.,”J. Comput. Syst. Sci., vol. 72, pp. 648–659, 2006.
[12] U. Feige, D. Peleg, P. Raghavan, and E. Upfal, “Randomized broadcast in networks.,”Proc. 1st SIGAL Int. Symp. Algorithms, vol. 450, pp. 128–137, 1990.
[13] P. Fraigniaud and S. Vial, “Approximation algorithms for broadcasting and gossiping.,”J. Parallel Distrib. Comput., vol. 43, pp. 47–55, 1997.
[14] R. Beier and J. Sibeyn, “A powerful heuristic for telephone gossiping.,” Proc. 7th Int. Colloquium Structural Info Comm. Complexity, pp. 17–36, 2000.
[15] H. Harutyunyan and B. Shao, “An efficient heuristic for broadcasting in networks.,”J. Parallel Distrib. Comput., vol. 66, pp. 68–76, 2006.
[16] Y.-H. Su, C.-C. Lin, and D. Lee, “Broadcasting in weighted trees under the postal model,” Theor. Comput. Sci., vol. 621, pp. 73–81, 2016.
[17] C.-H. Tsou, G.-H. Chen, H.-I. Yu, and C.-C. Lin, “The broadcast median problem in heterogeneous postal model,” J. Comb Optim, vol. 25, no. 4, pp. 602–616, 2013.
[18] A. N. C. Kang and D. A. Ault, “Some properties of a centroid of a free tree,” Information Processing Letters, vol. 4, no. 1, pp. 18–20, 1975.
[19] A. J. Goldman, “Optimal center location in simple networks,” Transportation Science, vol. 5, pp. 212–221, 1971.
[20] S. Peng and W.-T. Lo, “Efficient algorithms for finding a core of a tree with a specified length,” Journal of Algorithms, vol. 20, pp. 445–458, 1996.
[21] P. M. Fenwick, “A new data structure for cumulative frequency tables,” SOFTWARE PRACTICE AND EXPERIENCE, vol. 24, no. 3, pp. 327–336, 1994.
[22] A. Tamir, “An O(pn^2) algorithm for the p-median and related problems on tree graphs,” Operations Research Letters, vol. 19, pp. 59–64, 1996.
dc.identifier.urihttp://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70275-
dc.description.abstract本論文提出一 O(n√n log n) 時間複雜度的演算法,來解決傳遞規則是異質郵寄模型的加權樹狀結構下的廣播雙重心問題。首先證明樹的中點是最佳的廣播中心,其次發現在廣播雙重心下,必定有一條邊是不會用到的,因此對每條邊兩側的子樹去計算廣播時間,最後應用樹狀數組的技巧,把子樹重複的部分合併計算而達到較佳的時間複雜度。zh_TW
dc.description.abstractThis thesis presents an O(n√n log n) time complexity algorithm for solving broadcast 2-medians problem on a weighted tree under the postal model. First,we prove that a centroid is the broadcast 1-median. Next, we can observe
that in broadcast 2-median, there exists an unused edge, so we compute thebroadcast time for the subtree of each edge in both side. Finally, for best time complexity, binary indexed tree data structure is used to compute the broadcast time, which can save time from recomputing the duplicated part of
subtree.
en
dc.description.provenanceMade available in DSpace on 2021-06-17T04:25:07Z (GMT). No. of bitstreams: 1
ntu-107-R05922092-1.pdf: 979374 bytes, checksum: 7e7e223b17b201be42cb27bc844fad81 (MD5)
Previous issue date: 2018
en
dc.description.tableofcontents誌謝 v
摘要 vii
Abstract ix
1 Introduction 1
1.1 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Notations and definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Finding Broadcast 1-Median 5
3 Finding Broadcast 2-Medians 11
3.1 The case of subtrees without centroid . . . . . . . . . . . . . . . . . . . 12
3.2 The case of subtrees with centroid . . . . . . . . . . . . . . . . . . . . . 23
4 Conclusion and Future Work 35
Bibliography 37
dc.language.isoen
dc.subject中點zh_TW
dc.subject廣播重心zh_TW
dc.subject異質郵寄模型zh_TW
dc.subject樹狀數組zh_TW
dc.subject階躍函數zh_TW
dc.subjectcentroiden
dc.subjectbinary indexed treeen
dc.subjectstep functionen
dc.subjectheterogeneous postal modelen
dc.subjectbroadcast medainen
dc.title加權樹上基於郵政模型的廣播雙重心問題zh_TW
dc.titleFinding Broadcast 2-Medians on a Weighted Tree under
the Postal Model
en
dc.typeThesis
dc.date.schoolyear106-2
dc.description.degree碩士
dc.contributor.coadvisor林清池
dc.contributor.oralexamcommittee張貴雲,傅榮勝
dc.subject.keyword廣播重心,異質郵寄模型,中點,樹狀數組,階躍函數,zh_TW
dc.subject.keywordbroadcast medain,heterogeneous postal model,centroid,binary indexed tree,step function,en
dc.relation.page39
dc.identifier.doi10.6342/NTU201802639
dc.rights.note有償授權
dc.date.accepted2018-08-15
dc.contributor.author-college電機資訊學院zh_TW
dc.contributor.author-dept資訊工程學研究所zh_TW
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