arXiv subjects

Tuukka Korhonen

Publications and source records attributed to Tuukka Korhonen.

39 records · Page 3Linked to original sources

arXiv2020

Listing Small Minimal Separators of a Graph

Let $G$ be a graph and $a,b$ vertices of $G$. A minimal $a,b$-separator of $G$ is an inclusion-wise minimal vertex set of $G$ that separates $a$ and $b$. We consider the problem of enumerating the minimal $a,b$-separators of $G$ that contain at most $k$ vertices, given some integer $k$. We give an algorithm which enumerates such minimal separators, outputting the first $R$ minimal separators in at most $poly(n) R \cdot \min(4^k, R)$ time for all $R$. Therefore, our algorithm can be classified as fixed-parameter-delay and incremental-polynomial time. To the best of our knowledge, no algorithms with non-trivial time complexity have been published for this problem before. We also discuss barriers for obtaining a polynomial-delay algorithm.

cs.DS↗

arXiv2020

Tight Bounds for Potential Maximal Cliques Parameterized by Vertex Cover

We show that a graph with $n$ vertices and vertex cover of size $k$ has at most $4^k + n$ potential maximal cliques. We also show that for each positive integer $k$, there exists a graph with vertex cover of size $k$, $O(k^2)$ vertices, and $Ω(4^k)$ potential maximal cliques. Our results extend the results of Fomin, Liedloff, Montealegre, and Todinca [Algorithmica, 80(4):1146--1169, 2018], who proved an upper bound of $poly(n) 4^k$, but left the lower bound as an open problem.

math.CO↗

arXiv2020

SMS in PACE 2020

We describe SMS, our submission to the exact treedepth track of PACE 2020. SMS computes the treedepth of a graph by branching on the small minimal separators of the graph.

cs.DS↗