DateLine: Efficient Algorithm for Computing Region Disjoint Paths in Backbone Networks

Survivable routing is crucial in backbone networks to ensure connectivity, even during failures. During network design, groups of network elements prone to potential failure events are identified. These groups are referred to as Shared Risk Link Groups (SRLGs). When these SRLGs consist of a set of links intersected by a connected region of the plane, they are termed regional-SRLGs. A recent study has presented a polynomial-time algorithm for finding a maximum number of regional-SRLG-disjoint paths between two given nodes in a planar topology, where the paths are node-disjoint. However, existing algorithms for this problem are not practical due to their runtime and implementation complexities. This paper investigates a more general model in two aspects. First, instead of node-disjointness, we search for non-crossing regional-SRLG-disjoint paths. Second, we show how the algorithm can be extended to solve problems in directed networks. It introduces an efficient and easily implementable algorithmic framework, leveraging an arbitrarily chosen shortest path finding subroutine for graphs with possibly negative weights. Depending on the subroutine chosen, the framework either improves the previous worst-case runtime complexity or can solve the problem with high probability (w.h.p.) in near-linear expected time. The proposed framework enables the first additive approximation for a more general $\mathscr {N}$ $\mathscr {P}$ -hard version of the problem, where the objective is to find the maximum number of regional-SRLG-disjoint paths. We validate our findings through extensive simulations.