Discrete Mathematics - Topics on domination
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
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Minimum connected dominating sets and maximal independent sets in unit disk graphs
Theoretical Computer Science
Ad hoc networks beyond unit disk graphs
Wireless Networks
Algorithmic models for sensor networks
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
On the minimization of the number of forwarding nodes for multicast in wireless ad hoc networks
ICCNMC'05 Proceedings of the Third international conference on Networking and Mobile Computing
Approximating fault-tolerant Steiner subgraphs in heterogeneous wireless networks
Proceedings of the 6th International Wireless Communications and Mobile Computing Conference
Maximising lifetime for fault-tolerant target coverage in sensor networks
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
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Multicast communication in a wireless ad-hoc network can be established using a tree that spans the multicast sender and receivers as well as other intermediate nodes. If the network is modelled as a graph, the multicast tree is a Steiner tree, the multicast sender and receivers correspond to terminals, and other nodes participating in the tree are Steiner nodes. As Steiner nodes are nodes that participate in the multicast tree by forwarding packets but do not benefit from the multicast, it is a natural objective to compute a tree that minimizes the total cost of the Steiner nodes. We therefore consider the problem of computing, for a given node-weighted graph and a set of terminals, a Steiner tree with Steiner nodes of minimum total weight. For graph classes that admit spanning trees of maximum degree at most d, we obtain a 0.775d-approximation algorithm. We show that this result implies a 3.875-approximation algorithm for unit disk graphs, an O(1/α2)-approximation algorithm for α-unit disk graphs, and an O(λ)-approximation algorithm for (λ + 1)-claw-free graphs.