An FPRAS for two terminal reliability in directed acyclic graphs

TL;DR

This paper presents an efficient randomized algorithm to approximate two-terminal reliability in DAGs, while also establishing the computational hardness of approximating unreliability in the same context.

Contribution

The paper introduces an FPRAS for two-terminal reliability in DAGs and proves the hardness of approximating unreliability, advancing understanding of reliability computation complexity.

Findings

FPRAS for two-terminal reliability in DAGs

Hardness result for unreliability approximation in DAGs

Complexity distinction between reliability and unreliability

Abstract

We give a fully polynomial-time randomized approximation scheme (FPRAS) for two terminal reliability in directed acyclic graphs (DAGs). In contrast, we also show the complementing problem of approximating two terminal unreliability in DAGs is #BIS-hard.