This Article 
 Bibliographic References 
 Add to: 
Energy-Efficient Permutation Routing in Radio Networks
June 2001 (vol. 12 no. 6)
pp. 544-557

Abstract—A radio network (RN, for short) is a distributed system populated by small, hand-held commodity devices running on batteries. Since recharging batteries may not be possible while on mission, we are interested in designing protocols that are highly energy efficient. One of the most effective energy-saving strategies is to mandate that the stations go to sleep whenever they do not transmit or receive messages. It is well known that a station is expending power while its transceiver is active, that is, while transmitting or receiving a packet. It is perhaps surprising at first that a station is expending power even if it receives a packet that is not destined for it. Since, in single-hop radio networks, every station is within transmission range from every other station, the design of energy-efficient protocols is highly nontrivial. An instance of the permutation routing problem involves $p$ stations of an RN, each storing ${n \over p}$ items. Each item has a unique destination which is the identity of the station to which the item must be routed. The goal is to route all the items to their destinations while expending as little energy as possible. Since, in the worst case, each item must be transmitted at least once, every permutation routing protocol must take ${n\over k}$ time slots. Similarly, each station must be awake for at least ${n\over p}$ time slots to transmit and/or receive packets. Our main contribution is to present an almost optimal energy-efficient permutation routing protocol for a $k \hbox {-} {\rm channel}$, a $p \hbox {-} {\rm station}$ RN that routes $n$ packets in at most $(2d+2b+1){n\over k}+k$ time slots with no station being awake for more than $(4d+7b-1){n\over p}$ time slots, where $d=\left\lceil{\log {p\over k}\over \log {n\over p}}\right\rceil$, $b=\left\lceil{\log k\over \log {n\over p}}\right\rceil$, and $k\leq \sqrt{p\over 2}$. Since, in most real-life situations, the number $n$ of packets to route, the number $p$ of stations in the RN, and the number $k$ of channels available satisfy the relation $k \ll p \ll n$, it follows that $d$ and $b$ are very small.

[1] Multiple Access Communications: Foundations for Emerging Technologies. N. Abramson, ed. New York: IEEE, 1993.
[2] N. Abramson, “Multiple Access in Wireless Digital Networks,” Proc. IEEE, vol. 82, pp. 1,360–1,370, 1994.
[3] N. Alon, A. Bar-Noy, N. Linial, and D. Peleg, “Single-Round Simulation on Radio Networks,” J. Algorithms, vol. 13, pp. 188–210, 1992.
[4] A. Bagchi and S. Hakimi, "Data Transfers in Broadcast Networks," IEEE Trans. Computers, vol. 41, no. 7, pp. 842-847, July 1992.
[5] D.J. Baker, “Data/Voice Communication over a Multihop, Mobile, High Frequency Network,” Proc. Military Comm. Conf. '97, pp. 339-343, 1997.
[6] N. Bambos and J.M. Rulnick, “Mobile Power Management for Wireless Communication Networks,” Wireless Networks, vol. 3, pp. 3–14, 1997.
[7] R. Bar-Yehuda, O. Goldreich, and A. Itai, “Efficient Emulation of Single-Hop Radio Network with Collision Detection on Multi-Hop Radio Network with No Collision Detection,” Distributed Computing, vol. 5, pp. 67-71, 1991.
[8] R. Bar-Yehuda, O. Goldreich, and A. Itai, “On the Time-Complexity of Broadcast in Multi-Hop Radio Networks: An Exponential Gap between Determinism and Randomization,” J. Computer and Systems Sciences, vol. 45, pp. 104–126, 1992.
[9] D. Bertzekas and R. Gallager, Data Networks, second ed. Prentice-Hall, 1992.
[10] U. Black, Mobile and Wireless Networks. Upper Saddle River, N.J.: Prentice-Hall, 1996.
[11] J.L. Bordim, J. Cui, T. Hayashi, K. Nakano, and S. Olariu, “Energy-Efficient Initialization Protocols for Ad-Hoc Radio Networks,” Proc. Int'l Symp. Algorithms and Computation, pp. 215–224, Dec. 1999.
[12] S. Craver, B.L. Yeo, and M.M. Yeung, "Digital Watermarking—Technical Trials and Legal Tribulations," Comm. ACM, Vol. 41, No. 7, July 1998, pp. 45-54.
[13] P.H. Dana, “The Geographer's Craft Project,” Dept. of Geography, Univ. of Texas, Austin, gpsgps.html, Sept. 1999.
[14] B.H. Davies and T.R. Davies, “Applications of Packet Switching Technology to Combat Net Radio,” Proc. IEEE, vol. 75, pp. 43-55, 1987.
[15] D. Duchamp, S.K. Feiner, and G.Q. Maguire, “Software Technology for Wireless Mobile Computing,” IEEE Network Magazine, pp. 12–18, Nov. 1991.
[16] W.C. Fifer and F.J. Bruno, “Low Cost Packet Radio,” Proc. IEEE, vol. 75, pp. 33-42, 1987.
[17] M. Fine and F.A. Tobagi, “Demand Assignment Multiple Access Schemes in Broadcast Bus Local Area Networks,” IEEE Trans. Computers, vol. 33, pp. 1130-1159, 1984.
[18] W.R. Franta and M.B. Bilodeau, “Analysis of Prioritized CSMA Protocol Based on Staggered Delays,” Acta Informatica, vol. 13, pp. 299-324, 1980.
[19] W.R. Franta and J.R. Heath, “Measurement and Analysis of HYPERchannel Networks,” IEEE Trans. Computers, vol. 33, pp. 1124-1130, 1984.
[20] M. Gerla and T.-C. Tsai, “Multicluster, Mobile, Multimedia Radio Network,” Wireless Networks, vol. 1, pp. 255–265, 1995.
[21] M.D. Grammatikakis, D.F. Hsu, M. Kraetzl, and J. Sibeyn, “Packet Routing in Fixed-Connection Networks: A Survey,” J. Parallel and Distributed Computing, pp. 77–132, 1998.
[22] T. Han and D.F. Stanat, “'Move and Smooth' Routing Algorithms on Mesh-Connected Computers,” Proc. 28th Ann. Allerton Conf. Comm., Control, and Computing, pp. 236-245, 1990.
[23] J.C. Haartsen, “The Bluetooth Radio System,” IEEE Personal Comm., vol. 7, no. 1, pp. 28-36, Feb. 2000.
[24] E.P. Harris and K.W. Warren, “Low Power Technologies: A System Perspective,” Proc. Third Int'l Workshop Multimedia Comm., 1996.
[25] A. Iwata, C.-C. Chiang, G. Pei, M. Gerla, and T.-W. Chen, “Scalable Routing Strategies for Ad hoc Networks,” IEEE J. Selected Areas in Comm., vol. 17, pp. 1,369–1,379, 1999.
[26] S.L. Johnsson and C.T. Ho,“Spanning graphs for optimum broadcasting and personalizedcommunication in hypercubes,” IEEE Trans. Computers, vol. 38, no. 9, pp. 1,249-1,268, Sept. 1989.
[27] E.D. Kaplan, Understanding GPS: Principles and Applications. Boston: Artech House, 1996.
[28] Y.B. Ko and N.H. Vaidya, “Location-Aided Routing (LAR) in Mobile Ad Hoc Networks,” Proc. Conf. Mobile Computing MOBICOM, pp. 66-75, 1998.
[29] D.H. Lawrie, “Access and Alignment of Data in an Array Processor,” IEEE Trans. Computers, vol. 24, pp. 1145-1155, 1975.
[30] C.R. Lin and M. Gerla, “Adaptive Clustering in Mobile Wireless Networks,” IEEE J. Selected Areas in Communications, vol. 16, pp. 1,265–1,275, 1997.
[31] W. Mangione-Smith and P.S. Ghang, “A Low Power Medium Access Control Protocol for Portable Multimedia Devices,” Proc. Third Int'l Workshop Mobile Multimedia Comm., Sept. 1996.
[32] K. Nakano and S. Olariu, “Randomized Initialization Protocols for Radio Networks,” IEEE Trans. Parallel and Distributed Systems, pp. 749-759 Nov. 2000
[33] K. Nakano and S. Olariu, “Randomized$O(\log\log n)$-Round Leader Election Protocols in Packet Radio Networks,” Proc. Int'l Symp. Algorithms and Computation, pp. 209–218, 1998.
[34] K. Nakano, S. Olariu, and J.L. Schwing, “Broadcast-Efficient Algorithms on the Coarse-Grain Broadcast Communication Model with Few Channels,” Proc. Int'l Parallel Processing Symp., pp. 31-35, 1998.
[35] K. Nakano, S. Olariu, and J. L. Schwing, “Broadcast-Efficient Protocols for Ad-Hoc Radio Networks with Few Channels,” IEEE Trans., Parallel and Distributed Systems, vol. 12, pp. 1,276-1,289, 1999.
[36] M. Joa-Ng and I.-T. Lu, “A Peer-to-Peer Zone-Based Two-Level Link State Routing for Mobile Ad Hoc Networks,” IEEE J. Selected Areas in Comm., vol. 17, pp. 1415–1425, 1999.
[37] B. Parhami, Introduction to Parallel Processing. Plenum, 1999.
[38] B. Parkinson and S. Gilbert, “NAVSTAR: Global Positioning System—Ten Years Later,” Proc. IEEE, vol. 71, pp. 1177-1186, 1983.
[39] R.A. Powers, “Batteries for Low-Power Electronics,” Proc. IEEE, vol. 83, pp. 687-693, 1995.
[40] R. Ramanathan and M. Steenstrup, “Hierarchically-Organized, Multihop Wireless Networks for Quality-of-Service Support,” Mobile Networks and Applications, vol. 3, pp. 101–119, 1998.
[41] D. Raychaudhuri and N.D. Wilson, "ATM-Based Transport Architecture for Multiservices Wireless Personal Communication Network," IEEE J. Selected Areas Comm., vol. 12, no. 8, Oct. 1994, pp. 4101-1414.
[42] A.K. Salkintzis and C. Chamzas, “An In-Band Power-Saving Protocol for Mobile Data Networks,” IEEE Trans. Comm., pp. 1,194–1,205, 1998.
[43] R. Sanchez, J. Evans, and G. Minden, “Networking on the Battlefield: Challenges in Highly Dynamic Multihop Wireless Networks,” Proc. IEEE MILCOM '99, Oct. 1999.
[44] S. Singh and C.S. Raghavendra, “PAMAS—Power Aware Multi-Access Protocol with Signalling for Ad Hoc Networks,” Proc. ACM SIGCOMM, Computer Comm. Rev., July 1998.
[45] K. Sivalingam, M.B. Srivastava, and P. Agrawal, “Low Power Link and Access Protocols for Wireless Multimedia Networks,” Proc. IEEE Vehicular Technology Conf., (VTC '97), May 1997.
[46] D. Steinberg, “Note on Invariant Properties on the Shuffle Exchange and a Simplified Cost-Effective Version of the Omega Network,” IEEE Trans. Computers, vol. 32, pp. 444-453, 1983.
[47] M. Stemm, P. Gauthier, and D. Harada, “Reducing Power Consumption on Network Interfaces in Hand-Held Devices,” Proc. Third Int'l Workshop Multimedia Comm., 1996.
[48] F. Tobagi and V.B. Hunt, “Performance Evaluation of Carrier Sense Multiple Access with Collision Detection,” Computer Networks, vol. 4, pp. 435-467, 1980.
[49] J.E. Wieselthier, G.D. Nguyen, and A. Ephemerides, “Multicasting in Energy-Limited Ad-Hoc Wireless Networks,” Proc. MILCOM '98, 1998.

Index Terms:
Radio networks, rapidly deployable networks, wireless communications, energy-efficient protocols, reservation protocols, permutation routing.
Koji Nakano, Stephan Olariu, Albert Y. Zomaya, "Energy-Efficient Permutation Routing in Radio Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 12, no. 6, pp. 544-557, June 2001, doi:10.1109/71.932709
Usage of this product signifies your acceptance of the Terms of Use.