On the Probability of Finding Non-interfering Paths in Wireless Multihop Networks

Multipath routing can improve system performance of capacity-limited wireless networks through load balancing. However, even with a single source and destination, intra-flow and inter-flow interference can void any performance improvement. In this paper, we show that establishing non-interfering paths can, in theory, leverage this issue. In practice however, finding non-interfering paths can be quite complex. In fact, we demonstrate that the problem of finding two non-interfering paths for a single source-destination pair is NP-complete. Therefore, an interesting problem is to determine if, given a network topology, non-interfering multipath routing is appropriate. To address this issue, we provide an analytic approximation of the probability of finding two non-interfering paths. The correctness of the analysis is verified by simulations.