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- W3104213686 abstract "Let $G=(V,E)$ be an undirected unweighted graph on $n$ vertices and $m$ edges. We address the problem of fault-tolerant data structure for all-pairs mincuts in $G$ defined as follows. Build a compact data structure that, on receiving a pair of vertices $s,tin V$ and any edge $(x,y)$ as query, can efficiently report the value of the mincut between $s$ and $t$ upon failure of the edge $(x,y)$. To the best of our knowledge, there exists no data structure for this problem which takes $o(mn)$ space and a non-trivial query time. We present two compact data structures for this problem. - Our first data structure guarantees ${cal O}(1)$ query time. The space occupied by this data structure is ${cal O}(n^2)$ which matches the worst-case size of a graph on $n$ vertices. - Our second data structure takes ${cal O}(m)$ space which matches the size of the graph. The query time is ${cal O}(min(m,n c_{s,t}))$ where $c_{s,t}$ is the value of the mincut between $s$ and $t$ in $G$. The query time guaranteed by our data structure is faster by a factor of $Omega(sqrt{n})$ compared to the best known algorithm to compute a $(s,t)$-mincut." @default.
- W3104213686 created "2020-11-23" @default.
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- W3104213686 date "2020-11-06" @default.
- W3104213686 modified "2023-09-27" @default.
- W3104213686 title "Fault-Tolerant All-Pairs Mincuts." @default.
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- W3104213686 hasPublicationYear "2020" @default.
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