在區塊圖上解決中央點與中心點問題之研究
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(2) On the Study of the Median and Center Problems on Block Graphs : NSC 87-2213-E-011-024 : 86 8 1 87 7 31 : !"# $%&'()*+ ,-./0 E-mail : [email protected]. 67589: ;<=>1?@. 67{ ~AhTUF 1ÔA67;
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(8) 2. F h67A1. ;H} P67 R¡¢ [;£ = h1B ¤. Abstract. ¥¦§ F¨1670©ª«JB. ;£ ¬}67h1¡¢A6. Location on networks is a topic of great importance in the fields such as. 7®¯°±¦±²³´F167 A ®²³µ´h} 67 T* ¡¢ A¶ ·F =1®²³µ¸¦±°¹´h}. transportation, communication, service areas. 67Aº1h1»¼67Fk 1½¾¿À>ÁÂÃĮű¦±¦Æ´mÇÈ. criteria in which the distance to the farthest vertex from the site is minimized and. ÉAF67Ar ~®Ê¯±´; >}r ]AT^7ËÌÍFÎ1. A
(9) Ï®¦ÊÊÆ´;>} |. minsum criteria in which the total distance to the vertices from the site is minimized. Let u and v be two vertices in a graph G.. 67A TÌ~FmÐ
(10). ®¦´;>} 67Ñ"T^A. A graph G is connected if G contains a u-v path for every pair u, v of vertices of G. A.
(11) ÏÒÎ ®Óʱ´>} |. vertex v is called a cut vertex if removing v. 12345. and computer sciences. The criteria for locating problem in literature are minmax. 1.
(12) and all edges incident to it increases the number of components. A connected graph. . without a cut vertex is called a nonseparable graph. A block of a graph is a maximal nonseparable graph. A graph is called a. A]ôÞßàc67Ano;¡ ¢gä[gAFD;SA 5þAÕÞß67A[;. block graph if every block of the graph is complete. The concept of block graph was. O
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(14) A. first introduced by Harary. For a graph G and a pair u, v of vertices of G, the distance d(u, v) between u and v is the length of a. F 2à o. shortest u-v path in G if such a path exists. The eccentricity, e(v), of a vertex v is the. . farthest distance from v to any vertex of G. A vertex v with minimum e(v) is called a The sum of the distances from. A+ a;1í v@5A FGH 7W[; HJ891KL OP LQRSTU2. u to each other vertex of G is denoted by D(u). A vertex u with minimum D(u) is. HJ1 ÕÖ1d ;P ! } | Aº"#~T^$$%%. called a median of G. On general graphs, the medians and. &HsA ;']1 +()*v+ÍAnoFY3, A-.;}s 5<pqhr/0. center of G.. Áþ67ÕÖ
(15). 675ÕÖ1TABC ;. centers of a graph can be found in O(n3) by using Floyd’s algorithm which solves the all. Fu1/;>ÖÕ167ÛcA
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(17) |67{ A~. pairs shortest path problem, where n is the number of vertices in a graph. On tree networks, however, more efficient. hT^; 5AgOPm34A\ ]hT^Fu/0;>5167 ÛcÕÖ ;12} |67{. algorithms can be devised to find the medians. Goldman proposed an efficient. A~hTU;ym67AþA OPLQARShTê8FÎk. algorithm to find the medians and centers of a tree in O(n) time [4]. In this project, we shall consider the problem of finding the. r/0â;+9ãY67AÛct ÉnoHJLg67S:ÛcA;ð;É ÕÖ"ì A/0F1ÔA. medians and centers in a block graph. Notice that tree networks are special cases. 67Ûcâm ÈÉAíî¢;þT åÙ<5%ÙA\];NO
(18). of blcok graphs. KeywordsNetworkmedianscenters. A FõDhH;=>+ 9?Î@AÞßA67ÛcÉÕÖÈT" ìAíî¢FBCÞßàcâ;OYï. block graph. . ðA\]És ;DE"1F G;12Þß67AÛc H[;". 2ýÁ þA. =>AgôF"I;ÕÖ1ä 2.
(19) [gA67Ûc_"ìA/Ù;2R hSñA 5JbmF. [3] F. Buckley and F. Harary, Distance in Graph, Addison-Wesley, Reading, MA,. K2R . 1990. [4] J. Goldman, Optimum center location in Simple Networks, Transportation. . LM"67AB;ðI LM67;×Ø!A½. Science, Vol. 5, 1971, pp. 212-221. [5] F. Harary, A Characterization of block. _ÞßàcA; ÉnoF NO
(20) 67A; ðIÁABPQ;ªR. graphs, Canadian Mathematical Bulletin, Vol. 6, 1963, pp. 1-6. [6] F. Harary and G. Prins, The. STA67Ûcâ;y.
(21) AUßV"ªRA;. block-cutpoint-tree of a graph. Publicationes Mathematicae Debrecen,. . ðFD;67ÛcA.
(22) UßV;>W noAF . ÇÈXYAíî¢IZA6. Vol. 13, 1966, pp. 103-107. [7] F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969.. 72
(23) %B;ðA no;?Î È"ìAÙ¢F. [8] P. B. Mirchandani and Aissa Oudjit, Localizing 2-Medians on Probabilistic. +;A67@5:. ÖÕ;1[\r] Fu1>; A[gA67Ûc1^"äåA. and Deterministic Tree Networks, Networks, Vol. 10, 1980, pp. 329-350. [9] Peng and W. Lo, Efficient Algorithms for. Ù¢É} Fu>;BC" äåAíî¢É}s ;Dø. Finding a Core of a Tree with a Specified Length, Journal of Algorithms, Vol. 20,. OgÞß67ÛcFD;S ñA_,; 5ÇÈ1"ì ÏAíî¢Ò /\]ú . 1996, pp. 445-458. [10] C. Tansel, R. L. Francis, and T. J. Lowe, Location on Networks: A survey,. ïðA\];R\}íî¢1Og `abA67ÛcÉ. Management Science, Vol. 29, 1983, pp. 482-511.. A F. . c2de3, [1] V. Aho, J. E. Hopcroft, and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974. [2] G. Chartrand, O. R. Oellermann, Applied and Algorithmic Graph Theory, McGraw-Hill, Reading, MA, 1993. 3.
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