Broadcasting in multi-radio multi-channel wireless networks using simplicial complexes

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.