Summary of Network Lifetime and Power Assignment in ad hoc Wireless Networks

In ad-hoc wireless networks, certain network connectivity constraints are of interest because of their practical importance. An example of such a constraint would be strong connectivity. The aim is usually to minimize the power used to maintain such connectivities by adjusting the transmission power of the nodes of the network. Such problems are called Power Assignment problems. Another set of similar problem classes called Network Lifetime problems arise if the nodes have initial battery supply depending on the node and the aim is to maintain a connectivity constraint as long as possible in the network. Calinescu et al.[1] give approximation algorithms for the Min-Power Symmetric Connectivity, Min-Power Strong Connectivity and Min-Power Broadcast and give a special treatment for the important case of MinPower Symmetric Connectivity in the Euclidean with node-dependent transmission efficiency. For Network Lifetime, an approximation algorithm is given based on the polynomial time approximation scheme (PTAS) for linear programs by Garg and Köneman.