论文标题
两端可靠性的根
Roots of Two-Terminal Reliability
论文作者
论文摘要
假设图$ g $的顶点始终运行，但是$ g $的边缘是独立运行的，概率$ p \ in [0,1] $。对于固定的顶点$ s $和$ t $，$ g $的\ emph {两端的可靠性}是操作子图包含$（s，t）$路径的概率，而\ emph {all-terminal of g $的$ g $的$ g $是$ g $的$ emph {s，t）。这两个可靠性都是$ p $的多项式，并且在许多方面都具有非常相似的行为。但是，与全末端的可靠性不同，对两个可函数多项式的根源知之甚少。我们将通过多种方式表明，两端可靠性多项式的根的性质和位置与全末端可靠性的根具有明显不同。
Assume that the vertices of a graph $G$ are always operational, but the edges of $G$ are operational independently with probability $p \in[0,1]$. For fixed vertices $s$ and $t$, the \emph{two-terminal reliability} of $G$ is the probability that the operational subgraph contains an $(s,t)$-path, while the \emph{all-terminal reliability} of $G$ is the probability that the operational subgraph contains a spanning tree. Both reliabilities are polynomials in $p$, and have very similar behaviour in many respects. However, unlike all-terminal reliability, little is known about the roots of two-reliability polynomials. In a variety of ways, we shall show that the nature and location of the roots of two-terminal reliability polynomials have significantly different properties than those held by roots of the all-terminal reliability.
