On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks Jeffrey E. Wieselthier, Gam D. Nguyen, and Anthony Ephremides IEEE INFOCOM 2000 Speaker: Chung-Hsien Hsu Presented at TKU Group Meeting Mar. 04, 2004

Outline Introduction Wireless Communications Model Minimum-Energy Broadcast Trees Broadcast Algorithm BIP (Broadcast Incremental Power Algorithm) BLU (Broadcast Least-Unicast-cost Algorithm) BLiMST (Broadcast Link-based MST Algorithm) Sweep Procedure Performance Results Conclusions

Introduction Focus: Source-initiated broadcasting and multicasting of session traffic. Objective: To form a minimum-energy tree. Jointed the issues of Physical layer and Network layer.

Wireless Communications Model Assumption: The power level of a transmission can be chosen within a given range of values. The availability of a large number of bandwidth resources. Sufficient transceiver resources are available at each of the nodes in the network. Using omnidirectional antennas. P ij = power needed for link between Node i and Node j = r α

Wireless Communications Model - Wireless Multicast Advantage Lind-based (wired networks) P i,(j,k) = P ij + P ik Node-based (wireless networks) P i,(j,k) = max{P ij, P ik } i j k P ij P ik

Minimum-Energy Broadcast Trees Wired Networks Link-based. Broadcast problem: MST (minimum-cost spanning tree) problem. Total coast: the sum of the link costs. Wireless Networks Node-based. Didn’t have any scalable solutions.

Minimum-Energy Broadcast Trees - Minimum-Energy Broadcasting: 2 Destinations Strategy (a): S -> D 2 Strategy (b): S -> D 1 -> D 2 Propagation: 1/r 2 Use strategy (a) if r 1 > r 2 cosθ Use strategy (b) otherwise S D1D1 D2D2 θ r1r1 r 12 r2r2

Minimum-Energy Broadcast Trees - Minimum-Energy Broadcasting: 2 Destinations Propagation: 1/r α Use strategy (a) if x α -1 < (1+x 2 -2xcosθ) α/2 where x = r 2 /r 1 Use strategy (b) otherwise S D1D1 D2D2 θ r1r1 r 12 r2r2

The Broadcast Incremental Power Algorithm Propagation : α=2

The Broadcast Incremental Power Algorithm BIP is similar in principle to Prim’s algorithm. One fundamental difference: The inputs to Prim’s algorithm are the link cost P ij. BIP must dynamically update the costs at each step. P ij ’ = P ij – P(i)

Broadcast Algorithm based on Link-Based Techniques – Broadcast Least-Unicast-cost (BLU) Algorithm BLU: A minimum-cost path from the source node to every other node is established (using Dijkstra algorithm...etc.) The broadcast tree consists of the superposition of these unicast paths. A straightforward but far from optimal approach. It is scalable.

Broadcast Algorithm based on Link-Based Techniques – Broadcast Least-Unicast-cost (BLU) Algorithm Propagation : α= P = 12.17

Broadcast Algorithm based on Link-Based Techniques – Broadcast Link-based MST (BLiMST) Algorithm BLiMST: A minimum-cost spanning tree. It is formed using standard (link-based) MST techniques. Ignored the “wireless multicast advantage”. It is scalable.

Broadcast Algorithm based on Link-Based Techniques – Broadcast Link-based MST (BLiMST) Algorithm Propagation : α=2 P =

Broadcast Algorithm – Complexity Considerations BLU: Dijkstra algorithm O(N 2 ) BLiMST: Prim’s algorithm O(N 3 ) BIP: Prim’s algorithm O(N 3 )

The Sweep: Removing Unnecessary Transmissions Sweep Procedure Examining the nodes in ascending ID order. Under investigation. Ignoring leaf nodes. The first sweep operation provides significant improvement.

The Sweep: Removing Unnecessary Transmissions - BIP Propagation : α=2 P = P = Before After

The Sweep: Removing Unnecessary Transmissions - BLU Propagation : α=2 P = P = Before After

The Optimal Tree Propagation : α= P = 6.30

Algorithms for Multicasting Multicast Incremental Power (MIP) Algorithm Multicast Least-Unicast-cost (MLU) Algorithm Multicast Link-based MST (MLiMST) Algorithm

Performance Results Environment: Number of nodes: 10 and 100 Region: 5x5 square region Randomly generate: Location of nodes Source node Multicast group size α: 2 and 4 Performance of 100 randomly generated networks.

Performance Results Performance metric: Normalized power Q i (m) = total power of multicast tree for network m, generated by algorithm i. Q best (m) = min {Q i (m)} Normalized power associated with algorithm i: Providing a measure of how close each algorithm comes to providing the lowest-power tree.

Performance Results

Conclusions Networking schemes should reflect the node- based nature of wireless communications. Proposed the Broadcast Incremental Power (BIP) Algorithm. Future works Development of distributed algorithms. To study the impact of limited bandwidth and transceiver resources. To develop mechanisms to cope with node mobility.

Prim’s algorithm a b h i c g d f e a b h i c g d f e a b h i c g d f e a b h i c g d f e

Dijkstra’s algorithm s t x zy s t x zy s t x zy s t x zy s t x zy s t x zy