Maximum-Lifetime Routing in Wireless Networks : System Optimization & Game-Theoretic Perspectives

A major problem in wireless networks is how to route traffic so as to maximize the lifetime of the transmission. We address a two-way multicast problem, where a root wishes to transmit data to a subset of nodes (called also terminals), which can also respond to the root. In addition, we consider the anycast problem, where there is a subset of nodes that can communicate with one another. We consider both directional antennas and omnidirectional antennas. First, we note that, for omnidirectional antennas, an optimal solution can be computed in polynomial time. Next, for directional antennas, we observe that computing an optimal solution is an NP-hard problem. Accordingly, we provide a polynomial time algorithm that finds a 2approximate solution for the case of uniform transmission power levels. For the much harder case, where there are different transmission power levels, we provide an O(log n) approximation algorithm for the general problem, and an O(log n) approximation algorithm for the special case where the set of terminals equals the set of all nodes. Next, we consider the corresponding noncooperative game scenarios, and prove that, by following the natural game course, users converge to a Nash equilibrium. For directional antennas, we show that the price of anarchy is unbounded. On the other hand, we show that the price of stability, where the best Nash equilibrium is considered, is 1; hence, optimal (networkwide) performance can be achieved if the initial configuration can be imposed on the players. For omnidirectional antennas, we show that, if the players join the game sequentially, the Nash equilibrium is (networkwide) optimal.

[1]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[2]  Ariel Orda,et al.  Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas , 2005, MobiHoc '05.

[3]  Christos H. Papadimitriou,et al.  Algorithms, Games, and the Internet (Extended Abstract) , 2001 .

[4]  Anthony Ephremides,et al.  On the construction of energy-efficient broadcast and multicast trees in wireless networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[5]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[6]  Éva Tardos,et al.  An approximation algorithm for the generalized assignment problem , 1993, Math. Program..

[7]  Nitin H. Vaidya,et al.  Performance of ad hoc routing using directional antennas , 2005, Ad Hoc Networks.

[8]  Martin Fürer,et al.  Approximating the Minimum-Degree Steiner Tree to within One of Optimal , 1994, J. Algorithms.

[9]  Anthony Ephremides,et al.  Energy-Aware Wireless Networking with Directional Antennas: The Case of Session-Based Broadcasting and Multicasting , 2002, IEEE Trans. Mob. Comput..

[10]  Radha Poovendran,et al.  Maximizing static network lifetime of wireless broadcast ad hoc networks , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[11]  Jean-Pierre Hubaux,et al.  Minimum-energy broadcast in all-wireless networks: NP-completeness and distribution issues , 2002, MobiCom '02.

[12]  R. Ravi,et al.  Approximation Through Local Optimality: Designing Networks with Small Degree , 1992, FSTTCS.

[13]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[14]  P. Gács,et al.  Algorithms , 1992 .

[15]  Wendi Heinzelman,et al.  Energy-efficient communication protocol for wireless microsensor networks , 2000, Proceedings of the 33rd Annual Hawaii International Conference on System Sciences.

[16]  Pekka Orponen,et al.  Multicast time maximization in energy constrained wireless networks , 2003, DIALM-POMC '03.

[17]  Tim Roughgarden,et al.  The price of stability for network design with fair cost allocation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[18]  Leandros Tassiulas,et al.  Energy conserving routing in wireless ad-hoc networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[19]  Andrzej Pelc,et al.  Power consumption in packet radio networks , 2000, Theor. Comput. Sci..

[20]  V. Georgiev.  Using Game Theory to Analyze Wireless Ad Hoc Networks . ” , 2008 .

[21]  Satish Kumar,et al.  Next century challenges: scalable coordination in sensor networks , 1999, MobiCom.

[22]  Gruia Calinescu,et al.  Network Lifetime and Power Assignment in ad hoc Wireless Networks , 2003, ESA.

[23]  Ramesh R. Rao,et al.  Energy-Efficient Routing Algorithms Using Directional Antennas for Mobile Ad Hoc Networks , 2002, Int. J. Wirel. Inf. Networks.

[24]  Jennifer C. Hou,et al.  On mitigating the broadcast storm problem with directional antennas , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[25]  Teresa H. Meng,et al.  Minimum energy mobile wireless networks , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).