On Minimizing the Total Power of K-Strongly Connected Wireless Networks

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Executive Summary

Given a wireless network, the authors want to assign each node a transmission power, which will enable transmission between any two nodes (via other nodes). Moreover, due to possible faults, they want to have at least k vertex-disjoint paths from any node to any other, where k is some fixed integer, depending on the reliability of the nodes. The goal is to achieve this directed k-strong connectivity with a minimal overall power assignment. The problem is NP-Hard for any k >= 1 already for planar networks. Here they first present an optimal power assignment for uniformly spaced nodes on a line for any k >= 1.

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