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The Burning Number of Directed Graphs: Bounds and Computational Complexity
Theory and Applications of Graphs, 2020 The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalizes naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for directed graphs,
Remie Janssen
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Parameterized Complexity of 1-Planarity [PDF]
Journal of Graph Algorithms and Applications, 2013 We consider the problem of drawing graphs with at most one crossing per edge. These drawings, and the graphs that can be drawn in this way, are called $1$-planar. Finding $1$-planar drawings is known to be ${\mathsf{NP}}$-hard, but we prove that it is fixed-parameter tractable with respect to the vertex cover number, tree-depth, and cyclomatic number ...
Bannister, Michael J. +2 more
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The Complexity of Reachability in Affine Vector Addition Systems with States [PDF]
Logical Methods in Computer Science, 2021 Vector addition systems with states (VASS) are widely used for the formal verification of concurrent systems. Given their tremendous computational complexity, practical approaches have relied on techniques such as reachability relaxations, e.g., allowing
Michael Blondin, Mikhail Raskin
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On the Average-case Complexity of Parameterized Clique [PDF]
, 2014 The k-Clique problem is a fundamental combinatorial problem that plays a prominent role in classical as well as in parameterized complexity theory. It is among the most well-known NP-complete and W[1]-complete problems.
Bollobás +22 more
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Parameterized parallel complexity [PDF]
, 1998 We introduce a framework to study the parallel complexity of parameterized problems, and we propose some analogs of NC.
Cesati M., Di Ianni M.
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Treewidth-based algorithms for the small parsimony problem on networks
Algorithms for Molecular Biology, 2022 Background Phylogenetic reconstruction is one of the paramount challenges of contemporary bioinformatics. A subtask of existing tree reconstruction algorithms is modeled by the Small Parsimony problem: given a tree T and an assignment of character-states
Celine Scornavacca, Mathias Weller
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Parameterized Complexity of Safe Set [PDF]
Journal of Graph Algorithms and Applications, 2019 In this paper we study the problem of finding a small safe set $S$ in a graph $G$, i.e., a non-empty set of vertices such that no connected component of $G[S]$ is adjacent to a larger component in $G - S$. We enhance our understanding of the problem from the viewpoint of parameterized complexity by showing that (1) the problem is W[2]-hard when ...
Rémy Belmonte +5 more
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Solving Integer Linear Programs by Exploiting Variable-Constraint Interactions: A Survey
Algorithms, 2019 Integer Linear Programming (ILP) is among the most successful and general paradigms for solving computationally intractable optimization problems in computer science.
Robert Ganian, Sebastian Ordyniak
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Completeness Results for Parameterized Space Classes
, 2013 The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy.
C.M.R. Kintala +10 more
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Parameterized complexity of MaxSat Above Average [PDF]
Theoretical Computer Science, 2012 In MaxSat, we are given a CNF formula $F$ with $n$ variables and $m$ clauses and asked to find a truth assignment satisfying the maximum number of clauses. Let $r_1,..., r_m$ be the number of literals in the clauses of $F$. Then $asat(F)=\sum_{i=1}^m (1-2^{-r_i})$ is the expected number of clauses satisfied by a random truth assignment (the truth ...
Crowston, Robert +4 more
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