Results 101 to 110 of about 364 (127)
Improved bounds for the excluded-minor approximation of treedepth [PDF]
SIAM Journal on Discrete Mathematics, 2019 Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for every positive integers $a,b$ and a graph $G$, if the ...
Wojciech Czerwinski +2 more
semanticscholar +8 more sources
Treedepth Inapproximability and Exponential ETH Lower Bound
CoRRTreedepth is a central parameter to algorithmic graph theory. The current state-of-the-art in computing and approximating treedepth consists of a $2^{O(k^2)} n$-time exact algorithm and a polynomial-time $O(\text{OPT} \log^{3/2} \text{OPT ...
Édouard Bonnet +2 more
semanticscholar +5 more sources
Weighted Treedepth is NP-complete on Graphs of Bounded Degree
CoRRA treedepth decomposition of an undirected graph $G$ is a rooted forest $F$ on the vertex set of $G$ such that every edge $uv\in E(G)$ is in ancestor-descendant relationship in $F$.
Jona Dirks +3 more
semanticscholar +3 more sources
Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters
International Colloquium on Automata, Languages and Programming, 2022 We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows: i) Binary CSP
H. Bodlaender +2 more
semanticscholar +7 more sources
Local search for valued constraint satisfaction parameterized by treedepth
CoRRSometimes local search algorithms cannot efficiently find even local peaks. To understand why, I look at the structure of ascents in fitness landscapes from valued constraint satisfaction problems (VCSPs) parameterized by the treedepth of their ...
Artem Kaznatcheev
semanticscholar +3 more sources
Computing Twin-Width via Treedepth and Vertex Integrity
Symposium on Theoretical Aspects of Computer ScienceTwin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes.
R. Ganian, Mathis Rocton
semanticscholar +4 more sources
Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space [PDF]
SIAM Journal on Discrete Mathematics, 2020 For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$.
Jesper Nederlof +3 more
semanticscholar +9 more sources
A Polynomial Excluded-Minor Approximation of Treedepth [PDF]
Journal of the European Mathematical Society, 2018 Treedepth is a well-studied graph invariant in the family of "width measures" that includes treewidth and pathwidth. Understanding these invariants in terms of excluded minors has been an active area of research.
K. Kawarabayashi, Benjamin Rossman
semanticscholar +3 more sources
A faster polynomial-space algorithm for Hamiltonian cycle parameterized by treedepth
CoRRA large number of NP-hard graph problems can be solved in $f(w)n^{O(1)}$ time and space when the input graph is provided together with a tree decomposition of width $w$, in many cases with a modest exponential dependence $f(w)$ on $w$. Moreover, assuming
Stefan Kratsch
semanticscholar +3 more sources
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MaxSAT-Based Postprocessing for Treedepth
International Conference on Principles and Practice of Constraint Programming, 2020Treedepth is an increasingly popular graph invariant. Many NP-hard combinatorial problems can be solved efficiently on graphs of bounded treedepth. Since the exact computation of treedepth is itself NP-hard, recent research has focused on the development of heuristics that compute good upper bounds on the treedepth.
Vaidyanathan Peruvemba Ramaswamy +1 more
semanticscholar +2 more sources