Abstract
The problem of finding k minimum energy, edge-disjoint paths in wireless networks (MEEP) arises in the context of routing and belongs to the class of range assignment problems. A polynomial algorithm which guarantees a factor-k-approximation for this problem has been presented before, but its complexity status was open. In this paper we prove that MEEP is NP-hard and give new lower and upper bounds on the approximation factor of the k-approximation algorithm. For MEEP on acyclic graphs we introduce an exact, polynomial algorithm which is then extended to a heuristic for arbitrary graphs.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Srinivas, A., Modiano, E.: Minimum Energy Disjoint Path Routing in Wireless Ad-Hoc Networks. In: Proc. Int. Conf. on Mobile Computing and Networking, pp. 122–133. ACM Press, New York (2003)
Singh, S., Woo, M., Raghavendra, C.S.: Power-Aware Routing in Mobile Ad Hoc Networks. In: Proc. Int. Conf. on Mobile computing and networking, pp. 181–190. ACM Press, New York (1998)
Suurballe, J.W.: Disjoint Paths in a Network. Networks 4, 125–145 (1974)
Ganesan, D., Govindan, R., Shenker, S., Estrin, D.: Highly-Resilient, Energy-Efficient Multipath Routing in Wireless Sensor Networks. SIGMOBILE Mob. Comput. Commun. Rev. 5(4), 11–25 (2001)
Nasipuri, A., Das, S.: On-Demand Multipath Routing for Mobile Ad Hoc Networks. In: Proc. Int. Conf. on Computer Communications and Networks, ICCCN’99, pp. 64–70 (1999)
Chen, W.T., Huang, N.F.: The Strongly Connecting Problem on Multihop Packet Radio Networks. IEEE Transactions on Communications 37(3), 293–295 (1989)
Lloyd, E.L., Liu, R., Marathe, M.V., Ramanathan, R., Ravi, S.S.: Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks. Mob. Netw. Appl. 10(1–2), 19–34 (2005)
Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power Consumption in Packet Radio Networks. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 363–374. Springer, Heidelberg (1997)
Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: Energy-Efficient Broadcast and Multicast Trees in Wireless Networks. Mob. Netw. Appl. 7(6), 481–492 (2002)
Clementi, A., Huiban, G., Penna, P., Rossi, G., Verhoeven, Y.: Some Recent Theoretical Advances and Open Questions on Energy Consumption in Ad-Hoc Wireless Networks. In: Proc. Workshop on Approximation and Randomization Algorithms in Communication Networks, ARACNE, pp. 23–38 (2002)
Tang, J., Xue, G.: Node-Disjoint Path Routing in Wireless Networks: Tradeoff between Path Lifetime and Total Energy. In: IEEE International Conference on Communications, vol. 7, pp. 3812–3816 (2004)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, London (1995)
Feige, U.: A Threshold of ln n for Approximating Set Cover. J. ACM 45(4), 634–652 (1998)
di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Englewood Cliffs (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Maier, M., Mecke, S., Wagner, D. (2007). Algorithmic Aspects of Minimum Energy Edge-Disjoint Paths in Wireless Networks. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-69507-3_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69506-6
Online ISBN: 978-3-540-69507-3
eBook Packages: Computer ScienceComputer Science (R0)