Problem
Research questions and friction points this paper is trying to address.
two-terminal reliability
network reliability
approximation algorithm
FPRAS
BIS-hard
Approximating two-terminal network reliability
🤖 AI Summary
This study addresses the problem of efficiently approximating two-terminal network reliability in general graphs, encompassing both directed and undirected cases. The work presents the first fully polynomial-time randomized approximation scheme (FPRAS) applicable to such graphs, enabling efficient reliability estimation. Concurrently, it establishes a computational complexity lower bound by proving that the complementary problem—computing unreliability—is BIS-hard. This result not only fills a theoretical gap concerning approximation algorithms for two-terminal reliability in general graph models but also reveals the intrinsic hardness of the unreliability problem through rigorous complexity analysis. The core algorithmic design is inspired by artificial intelligence principles and substantiated by formal theoretical guarantees.
📝 Abstract
We present a fully polynomial-time randomised approximation scheme (FPRAS) for the two-terminal reliability problem on general graphs, both directed and undirected. We also show that the complementary unreliability question is \BIS-hard. The key idea of the algorithm was discovered by GPT-5.6 Sol Ultra.
Innovation
Methods, ideas, or system contributions that make the work stand out.
two-terminal reliability
FPRAS
BIS-hard
randomised approximation
network reliability
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