在車用行動通訊網路(VANET)中，由於車輛快速移動的特性，容易造成無線網路中的封包遺失，進而影響網路的可靠度(reliability)。為了克服此問題，可以藉由提供多條不相交的路徑來提高可靠度。除此之外，若將節點的剩餘能量(residual energy)加入考量的條件中，節點間可能會有著非對稱的傳輸成本(communication cost)。在本論文中，我們將車用行動通訊網路中的節點劃分成兩類—重要的特殊節點(special node)與一般節點，所關心的問題是如何找到總權重最小且特殊節點間擁有多條不相交路徑的生成子圖(spanning subgraph)。我們分別討論車用行動通訊網路中，考慮對稱或者非對稱的傳輸成本，在特殊節點間的多條不相交的路徑所形成的四種不同拓樸形狀，以圖形模型定義相對應的最小權重問題，並且證明其中三種拓樸形狀的問題屬於NP-complete，而其中一種可在多項式時間得到最佳解。另外，對這個多項式時間可解的問題，我們提出一個啟發式的演算法(heuristic algorithm)，具有較低的計算複雜度。最後，我們對這四種最小權重問題進行效能評估，驗證所降低的總權重、增加的可靠度以及計算複雜度，確認了我們的演算法可得到總權重較小且可靠度較佳的解。

In this paper, we define four optimization problems according to various topology configurations in VANET. Furthermore, we give the NP-completeness proof for three of these problems, and proof that one is in polynomial time. We proposed two approaches for P-solvable problem, that is, optimal and heuristic approaches. In addition, we gave performance evaluations for all four problems and compared their performance.

[1] “Vadd: Vehicle-assisted data delivery in vehicular ad hoc networks,” vol. 57, no. 3, pp.
1–12, 2008.
[2] I. Saha, L. Sambasivan, S. Ghosh, and R. Patro, “Distributed fault tolerant topol-
ogy control in wireless ad-hoc sensor networks,” Wireless and Optical Communications
Networks, 2006 IFIP International Conference on, pp. 5 pp. –5, 2006.
[3] D. Berend, M. Segal, and H. Shpungin, “Power efficient resilience and lifetime in wireless
ad-hoc networks,” pp. 17–24, 2008.
[4] A. Srinivas and E. Modiano, “Minimum energy disjoint path routing in wireless ad-hoc
networks,” pp. 122–133, 2003.
[5] F. Wang, K. Xu, M. T. Thai, and D. Du, “Fault tolerant topology control for
one-to-all communications in symmetric wireless networks,” Int. J. Sen.
Netw., vol. 2, no. 3/4, pp. 163–168, 2007.
[6] F. Wang, M. Thai, Y. Li, X. Cheng, and D.-Z. Du, “Fault-tolerant topology control for
all-to-one and one-to-all communication in wireles networks,” Mobile Computing, IEEE
Transactions on, vol. 7, no. 3, pp. 322 –331, mar. 2008.
[7] M. Middendorf and F. Pfeiffer, “On the complexity of the disjoint paths problem,”
Combinatorica, vol. 13, no. 1, pp. 97–107, March 1993. [Online]. Available:
http://www.springerlink.com/content/m4152lv4527q8617
[8] E. M. Arkin and R. Hassin, “The k-path tree matroid and its applications to survivable
network design,” Discrete Optimization, vol. 5, no. 2, pp. 314–322, 2008.
[9] E. L. Lawler, “Matroid intersection algorithms,” Mathematical Programming, vol. 9,
no. 1, pp. 31–56, 1975.
[10] Y. Kobayashi and C. Sommer, “On shortest disjoint paths in planar graphs,” Discrete
Optimization, vol. 7, pp. 234–245, 2010, announced at ISAAC 2009.
[11] R. K. Wood, “Factoring algorithms for computing k-terminal network reliability,” Re-
liability, IEEE Transactions on, vol. 35, no. 3, pp. 269 –278, aug. 1986.
[12] S. Fortune, J. E. Hopcroft, and J. Wyllie, “The directed subgraph homeomorphism
problem,” Theor. Comput. Sci., vol. 10, pp. 111–121, 1980.
[13] E. Lawler, Combinatorial Optimization: Networks and Matroids. FortWorth: Saunders
College Publishing, 1976.
[14] A. Schrijver, P. Muidergracht, and A. Schrijver, “A course in combinatorial optimiza-
tion,” 2003.
[15] T. Ballardie, “Core based tree (cbt) multicast - architectural overview and specifica-
tion,” 1995.
[16] E. Schoch, F. Kargl, T. Leinmuller, and M.Weber, “Communication patterns in vanets,”
IEEE Communications Magazine, vol. 46, no. 11, pp. 119–125, November 2008.