On fault-tolerant path optimization under QoS constraint in multi-channel wireless networks

In multi-channel wireless networks, a fundamental problem is to find node-disjoint paths minimising global cost or the maximum individual path cost, under the constraint that each path operates on a separate channel to maximise the fault tolerance and robustness against channel instability and malicious attacks. Meanwhile, the quality of service (QoS) requirement (e.g., in terms of end-to-end delay) needs to be satisfied on each path. In this paper, we provide a comprehensive formulation and analysis on this multi-path optimization problem by casting it to the problem k-disjoint path with different colours (k-DPDC). We further formulate the Restricted MinSum k-DPDC and Restricted MinMax k-DPDC to denote the problems of finding multiple node- and channel-disjoint paths minimising the global cost and the maximum individual path cost under the QoS constraint on the path end-to-end delay. Given the NP-hardness of both problems, we focus on directed acyclic graphs and propose fully polynomial-time approximation algorithms for both problems.