Multicast lifetime maximization for energy-constrained wireless ad-hoc networks with directional antennas

Distributed Approximation Algorithms for Longest-Lived Multicast in WANETs with Directional Antennas

“…The lifetime of a multicast tree is typically defined as 1536-1276/10$25.00 c ⃝ 2010 IEEE the arc set of a multicast tree all arcs crossing a node partition ( , − ) such that ∈ and ∕ ⊂ a set of destination nodes a directed graph modeling the wireless network a multicast group, = { } ∪ a node set ( ) the node set of a multicast tree a multicast tree of ( , ) rooted at node an intermediate tree constructed by a distributed algorithm after the ( + 1)-th node or equivalently the -th arc ( ≥ 0) is added into the tree the size of a multicast group the number of nodes in the network the RF power needed for the link from node to node , min ≤ ≤ max the distance between node to node the transmission range required at to reach all its child nodes in and a node outside the node weight of at the snapshot the source node of multicast group the arc weight of ( , ) at the snapshot the propagation loss exponent ( ) the maximum arc weight of in a network with directional antennas ( ) the maximum arc weight of in a network with omni-directional antennas the residual energy of node the antenna beamwidth applied by node the minimum beamwidth required at to reach all its child nodes in and a node outside the upper bound of the approximation-ratio of the algorithm the maximal lifetime of an arc ( , ) ∈ at a given energy supply ( ) the minimum weight of arcs in Ω the family of all rooted multicast trees including nodes in (⋅) * an optimal solution the duration of the network operation time until the disconnection of the multicast tree due to the battery depletion. This optimization problem in networks with directional antennas has been studied in [13][14][15][16][17][18][19] and has been proven to be NPhard [19]. The exact solution for such a difficult problem is presented in [18] based a MILP (mixed integer linear programming) formulation.…”

“…Specifically, the cost of a link between nodes and is defined as = ⋅ ( (0)/ ( )) , where is the RF transmission power needed for the link from node to node , ( ) is the residual energy at node at time , and is a parameter that reflects the importance we assign to the impact of residual energy. The work in [13] uses a different approach from [16,17] with the lifetime as an explicit optimization objective. Similar to the greedy approach applied by Prim' algorithm, the proposed algorithm D-DPMT (Dynamic weight Directed Prime Multicast Tree) [13] increments a multicast tree by including one node at a time with proper antenna beam reconfiguration of its uplink node such that the included arc has the maximum lifetime at that iteration.…”

“…Their theoretical performance have been studied in [15]. Simulation results have also shown that these two distributed multicast algorithms for directional communications outperform other centralized multicast algorithms, e.g., [13,16,17], significantly.…”

“…Both problems have received substantial attentions, e.g., the work [1][2][3][4][5] for the first problem and [6][7][8][9][10][11][12][13][14][15][16][17][18][19] for the second. Although they are closely related, these two problems are not equivalent, i.e., a multicast tree with minimum energy consumption cannot guarantee that it has the maximum lifetime.…”

A Distributed Algorithm for Min-Max Tree and Max-Min Cut Problems in Communication Networks

“…The revised Dijkstra's algorithm [8] changes the relaxation operation given in (13) to the new one given in (14) as follows:…”