近幾年來，由於網路上資訊的爆炸，一些新的應用像是視訊會議、遠距教學等於是就被發展起來。這些多媒體應用通常都需要架構在有提供服務品質（QoS）保證的網路下。目前做品質服務（QoS）主要都是針對各種特定網路結構，採用一些猜測的方法，靠一連串的模擬(Simulation)作驗證。這是無法保證得到品質服務（QoS）的。所以研究如何達到品質服務（QoS）保證已經引起了廣大的注意。而有關網路骨幹的設計，往往會隨著所給定的條件而有所變化。
本篇論文主要是針對幾個網路設計的問題作一些探討，這幾個問題都有各自的需求。首先，我們先定義各問題，然後說明各個問題目前的研究成果。接著，我們將提出一個新的問題，也提供一個方法來解決並證明可達到不錯的效果。最後討論各問題還可以被研究的方向。

Due to the information explosion of internet, in recent years several new applications have been developed, such as video conferencing and distance learning. These applications often need to be built under the network structure that can offer the guaranteed quality of service. Traditionally, the guaranteed quality of service was obtained by doing a series of simulations by means of some heuristic algorithms under every specific network structure. It is becoming increasingly clear that traditional routing protocols are inadequate for these new applications which often have stringent quality of service （QoS）. Therefore, QoS is an important research area that has arrested much attention.
In this thesis, we will focus on several problems on network design. Every theme has its specific request and necessary. At first, we will re-define each theme in detail. Then we will survey these problems in turn and propose a new problem mixed with some of problems. Finally, the conclusions and the future work of all problem will be discussed.

[1] D. Gusfield, “Efficient methods for multiple sequence alignment with guaranteed error bounds”, Bull. Math, Biol. 55（1993）, pp 141-154.
[2] Zheng Wang, “On the complexity of quality of service routing”, Information Processing Letter, vol69, pp 111-114,1999.
[3] M. R. Garey and D. S. Johnson, “Computers and Intractability：A guide to the Theory of NP-Completeness,” Freeman, San Francisco, 1979.
[4] T. C. Hu, “Optimum communication spanning trees”, SIAM J. on Computing, 3（1974）,pp.188-195.
[5] Douglas B. West, Introduction to Graph Theory, Prentice-Hall, Inc., 1996.
[6] Zheng Wang, J. Crowcroft, “Bandwidth-delay based routing algorithms”, in: Proc. IEEE GlobeCom’95, Singapore, November 1995.
[7] B. Y. Wu, G. Lancia, V. Bafna, K. M. Chao, R. Ravi, and C. Y. Tang, ”A polynomial time approximation scheme for minimum routing cost spanning trees”, in the Proceedings of Ninth Annual ACM-SIAM Symposium on Discrete Algorithms（SODA’98）, pp.21-32, 1998
[8] B. Y. Wu, K. M. Chao, and C. Y. Tang, “Constructing light spanning trees with small routing cost”, in “Proceedings of the 16th International Symposium on Theoretical Aspects of Computer Science （STACS’99）,” Lecture Notes in Computer Science, Vol. 1563, pp.334-344, （Springer Verlag）, New York/Berlin, 1999.
[9] P. Pevzner, “Multiple alignment, communication cost, and graph matching”, SIAM J. Appl. Math. 52 （1992）, pp. 1763-1779.
[10] D. S. Johnson, J. K. Lenstra and A. H. G. Rinnooy Kan, “The complexity of the network design problem”, Networks, 8（1978）, pp. 279-285.
[11] D. Bertsekas, R. Gallager, Data Networks, Prentice-Hall, Englewood Cliffs, NJ, 1987.
[12] B. Y. Wu, G. Lancia, V. Bafna, K. M. Chao, R. Ravi, and C. Y. Tang, ”A polynomial time approximation scheme for minimum routing cost spanning trees”, SIAM J. Comput. Vol. 29, No. 3, 1999, pp. 761-778.
[13] B. Y. Wu, K. M. Chao, C. Y. Tang, ”Approximation algorithms for the shortest total path length spanning tree problems”, Discrete Applied Mathematics, 105（2000）, pp.273-289.
[14] S. Khuller, B. Raghavachari, and N. Young, “Balancing minimum spanning trees and shortest-path trees”, Algorithmica, 14（1995）, pp. 305-321.
[15] T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, the MIT Press, 1994.
[16] B. Y. Wu, K. M. Chao, C. Y. Tang, ”Approximation algorithms for some optimum communication spanning tree problems”, Discrete Applied Mathematics, 102（2000）, pp.245-266. Partial result of this paper appeared in the “Proceeding of the Ninth Annual International Symposium on Algorithm and Computation（ISAAC’98）,”Lecture Notes in Computer Science, Vol. 1553, pp. 407-416, （Springer Verlag）, New York/Berlin, 1998.
[17] V. Bafna, E. L. Lawler, P. Pevzner , ”Approximation Algorithms for Multiple Sequence Alignment”, Proceedings of the 5th Combinatorial Pattern Matching Conference, Lecture Notes in Computer Science, Vol. 807, Springer, Berlin, 1994, pp. 43-53.
[18] R. Wong, “Worst-case analysis of network design problem heuristics” , SIAM. Algebraic Discrete Methods , 1（1980）, pp. 51-63.
[19] M. L. Fredman and R. E. Tarjan, “Fibonacci heaps and their uses in improved network optimization algorithms”, Journal of the ACM, 34（3）（1987）, pp. 596-615.
[20] J. Jaffe, “Algorithms for finding paths with multiple constraints”, Networks 14（1984）, pp. 95-116.
[21] B. Y. Wu, K. M. Chao, and C. Y. Tang, ”A Polynomial Time Approximation Scheme for Optimum Product-Requirement Communication Spanning Trees”, J. Algorithms, 36（2000）, pp.182-204.
[22] J. Plesnik, “The complexity of designing a network with minimum diameter”, Networks, 11（1981）, pp. 77-85.
[23] E. L. Lawler, “Fast approximation algorithms for knapsack problems”, Math. Oper. Res. 4, No. 4 （1979）, pp. 339-356.
[24] B. Y. Wu, K. M. Chao, and C. Y. Tang, “Light Graphs with Small Routing Cost”, Technical Report, 2000.
[25] R. Hassin and A. Tamir, “On the minimum diameter spanning tree problem”, Information Processing Letters, 53（1995）, pp. 109-111.
[26] R. K. Ahuja, T. L, Magnanti, and J. B. Orlin, “Network Flows-Theory, Algorithms, and Applications”, Prentice-Hall, Englewood Cliffs, NJ, 1993.
[27] R. Dionne, M. Florian, “Exact and approximate algorithms for optimal network design”, Networks 9（1）（1979）, pp. 37-60.
[28] 國立清華大學資訊工程學系簡敦仁碩士論文
[29] 國立清華大學資訊工程學系吳邦一博士論文