WSNp1-7: Distributed Multicast Algorithms for Lifetime Maximization in Wireless Ad Hoc Networks with Omni-directional and 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.…”

“…This may result in extreme and unacceptable requirements on memory and computation capacities for a resource-constrained wireless multihop network. Two distributed maximum-lifetime algorithms DMMT-OA (Distributed Min-Max Tree algorithm for Omnidirectional Antennas) and DMMT-DA (Distributed Min-Max Tree algorithm for Directional Antennas) have been proposed in [14] for directional communications. Their theoretical performance have been studied in [15].…”

“…Our proposed DMMT-DA-NC algorithm can be implemented in a distributed manner, which is particularly beneficial to such networks. 2) Different from the traditional link-centric based distributed algorithm [14], the proposed DMMT-DA-NC algorithm can avoid some solutions that may be deviated far from optimal.…”

“…In this section, we first briefly overview existing distributed algorithms DMMT-OA/DMMT-DA [14] and then present a new one motivated by an important observation that can improve the performance of DMMT-DA. All distributed algorithms shall be described in a formal manner, which helps us understand the theoretical performance analysis in latter sections.…”

“…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.…”