A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Minimum-weight spanning tree algorithms a survey and empirical study
Computers and Operations Research
Minimum-energy broadcast in all-wireless networks: NP-completeness and distribution issues
Proceedings of the 8th annual international conference on Mobile computing and networking
Energy-efficient broadcast and multicast trees in wireless networks
Mobile Networks and Applications
Energy-efficient broadcast and multicast trees in wireless networks
Mobile Networks and Applications
Algorithm Design
Interference-aware topology control and QoS routing in multi-channel wireless mesh networks
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Approximate Minimum-Energy Multicasting in Wireless Ad Hoc Networks
IEEE Transactions on Mobile Computing
Routing and link-layer protocols for multi-channel multi-interface ad hoc wireless networks
ACM SIGMOBILE Mobile Computing and Communications Review
Algorithms for connected set cover problem and fault-tolerant connected set cover problem
Theoretical Computer Science
Channel assignment for multicast in multi-channel multi-radio wireless mesh networks
Wireless Communications & Mobile Computing - Next Generation Wireless Communications and Mobile Computing-Networking Technologies
Theoretical Computer Science
Multichannel mesh networks: challenges and protocols
IEEE Wireless Communications
Low-Latency Broadcast in Multirate Wireless Mesh Networks
IEEE Journal on Selected Areas in Communications
HPCC'07 Proceedings of the Third international conference on High Performance Computing and Communications
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We consider the broadcasting problem in multi-radio multi-channel ad hoc networks. The objective is to minimize the total cost of the network-wide broadcast, where the cost can be of any form that is summable over all the transmissions (e.g., the transmission and reception energy, the price for accessing a specific channel). Our technical approach is based on a simplicial complex model that allows us to capture the broadcast nature of the wireless medium and the heterogeneity across radios and channels. Specifically, we show that broadcasting in multi-radio multi-channel ad hoc networks can be formulated as a minimum spanning problem in simplicial complexes. We establish the NP-completeness of the minimum spanning problem and propose two approximation algorithms with order-optimal performance guarantee. The first approximation algorithm converts the minimum spanning problem in simplical complexes to a minimum connected set cover (MCSC) problem. The second algorithm converts it to a node-weighted Steiner tree problem under the classic graph model. These two algorithms offer tradeoffs between performance and time-complexity. In a broader context, this work appears to be the first that studies the minimum spanning problem in simplicial complexes and weighted MCSC problem.