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- W3205645355 abstract "Let $kappa(s,t)$ denote the maximum number of internally disjoint paths in an undirected graph $G$. We consider designing a data structure that includes a list of cuts, and answers in $O(1)$ time the following query: given $s,t in V$, determine whether $kappa(s,t) leq k$, and if so, return a pointer to an $st$-cut of size $leq k$ in the list. A trivial data structure includes a list of $n(n-1)/2$ cuts and requires $Theta(kn^2)$ space. We show that $O(kn)$ cuts suffice, thus reducing the space to $O(k^2 n+n^2)$. In the case when $G$ is $k$-connected, we show that $O(n)$ cuts suffice, and that these cuts can be partitioned into $O(k)$ laminar families; this reduces the space to $O(kn)$. The latter result slightly improves and substantially simplifies a recent result of Pettie and Yin [ICALP 2021]." @default.
- W3205645355 created "2021-10-25" @default.
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- W3205645355 date "2021-10-18" @default.
- W3205645355 modified "2023-09-27" @default.
- W3205645355 title "Data structure for node connectivity queries." @default.
- W3205645355 hasPublicationYear "2021" @default.
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