Alapfogalmak
Quasi-polynomial time approximation schemes for hypergraph unreliability are developed.
Kivonat
The hypergraph unreliability problem is introduced, extending graph unreliability studies.
Two algorithms are presented for hypergraph unreliability, providing estimators with bounded relative variance.
Theoretical challenges in approximating hypergraph unreliability are discussed.
The importance of hypergraphs in modeling real-world networks is highlighted.
The study initiates a new research direction in reliability analysis for hypergraphs.
Statisztikák
"For any fixed ε ∈(0, 1), there is a randomized Monte Carlo algorithm for the hypergraph unreliability problem that runs in mO(log n) time on an m-hyperedge, n-vertex hypergraph and returns an estimator X that satisfies X ∈(1 ± ε)uG(p) whp."
"For any fixed ε ∈(0, 1) and any δ ∈(0, 1), there is a randomized Monte Carlo algorithm for the hypergraph unreliability problem that runs in m · nO(log n·log log(1/δ)) time on an m-hyperedge, n-vertex hypergraph and returns an estimator X that satisfies X ∈(1 ± ε)uG(p) ± δ whp."
Idézetek
"The hypergraph unreliability problem is a natural generalization of network unreliability."
"Reliability problems are at the heart of analyzing the robustness of networks to random failures."