An Edge-Turbulence Algorithm for the 2-MRS Problem on Trees with Unreliable Edges

The sum-max 2-most reliable sources (Sum-Max 2-MRS) problem in a given unreliable network is referred to as finding a pair of nodes in the network from which the expected number of reachable nodes is maximized. This problem is #P-hard on general graphs and admits a cubic time algorithm on trees with unreliable edges. In this paper, we revisit the problem on trees and design an edge-turbulence algorithm with a quadratic time and quadratic spaces. Finally, we further develop an edge-turbulence based parallel algorithm with a lower time complexity.