A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Approximation algorithms
Distributed construction of connected dominating set in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
RMAC: A Reliable Multicast MAC Protocol for Wireless Ad Hoc Networks
ICPP '04 Proceedings of the 2004 International Conference on Parallel Processing
Supporting MAC Layer Multicast in IEEE 802.11 based MANETs: Issues and Solutions
LCN '04 Proceedings of the 29th Annual IEEE International Conference on Local Computer Networks
Minimizing broadcast latency and redundancy in ad hoc networks
IEEE/ACM Transactions on Networking (TON)
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In traditional multihop network broadcast problems, in which a message beginning at one node is efficiently relayed to all others, cost models typically used involve a charge for each unicast or each broadcast. These settings lead to a minimum spanning tree (MST) problem or the Connected Dominating Set (CDS) problem, respectively. Neglected, however, is the study of intermediate models in which a node can choose to transmit to an arbitrary subset of its neighbors, at a cost based on the number of recipients (due e.g. to acknowledgements or repeat transmissions). We focus in this paper on a transmission cost model of the form 1+Akb, where k is the number of recipients, b≥0, and A≥0, which subsumes MST, CDS, and other problems. We give a systematic analysis of this problem as parameterized by b (relative to A), including positive and negative results. In particular, we show the problem is approximable with a factor varying from 2+2H$#916; down to 2 as b varies from 0 to 1 (via a modified CDS algorithm), and thence with a factor varying from 2 to 1 (i.e., optimal) as b varies from 1 to $\log_2 (\frac{1}{A}+2)$ , and optimal thereafter (both via spanning tree). For arbitrary cost functions of the form 1+Af(k), these algorithms provide a 2+2H$#916; -approximation whenever f(k) is sublinear and a (1+A)/A-approximation whenever f(k) is superlinear, respectively. We also show that the problem is optimally solvable for any b when the network is a clique or a tree.