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- W1649663665 abstract "We show that minimum connected $(s,t)$-vertex separator ($(s,t)$-CVS) is $Omega(log^{2-epsilon}n)$-hard for any $epsilon >0$ unless NP has quasi-polynomial Las-Vegas algorithms. i.e., for any $epsilon >0$ and for some $delta >0$, $(s,t)$-CVS is unlikely to have $delta.log^{2-epsilon}n$-approximation algorithm. We show that $(s,t)$-CVS is NP-complete on graphs with chordality at least 5 and present a polynomial-time algorithm for $(s,t)$-CVS on bipartite chordality 4 graphs. We also present a $lceilfrac{c}{2}rceil$-approximation algorithm for $(s,t)$-CVS on graphs with chordality $c$. Finally, from the parameterized setting, we show that $(s,t)$-CVS parameterized above the $(s,t)$-vertex connectivity is $W[2]$-hard." @default.
- W1649663665 created "2016-06-24" @default.
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- W1649663665 date "2011-11-08" @default.
- W1649663665 modified "2023-09-26" @default.
- W1649663665 title "On the Complexity of Connected $(s,t)$-Vertex Separator" @default.
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- W1649663665 doi "https://doi.org/10.48550/arxiv.1111.1814" @default.
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