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Hitting forbidden induced subgraphs on bounded treewidth graphs
- MathematicsMFCS
- 2020
The smallest function $f_H(t)$ such that H-IS-Deletion can be solved in time is determined assuming the Exponential Time Hypothesis (ETH), and it is shown that when $H$ deviates slightly from a clique, the function suffers a sharp jump.
Tight conditional lower bounds for counting perfect matchings on graphs of bounded treewidth, cliquewidth, and genus
- Computer ScienceSODA
- 2016
It is proved that, assuming the counting version of the Strong Exponential-Time Hypothesis (#SETH), the problem of counting perfect matchings • has no (2 --- e)knO(1) time algorithm for any e > 0 on graphs of treewidth k (but it can be solved in time O(nk+1) if a k-expression is given).
Double-Exponential and Triple-Exponential Bounds for Choosability Problems Parameterized by Treewidth
- Computer Science, MathematicsICALP
- 2016
A matching lower bound is given giving evidence that double-exponential dependence on treewidth may be necessary for the choosability problem, and evidence that an algorithm with running time 2^(2^(o(w)))*n^(O(1)) would violate the Exponential-Time Hypothesis (ETH).
Finding List Homomorphisms from Bounded-treewidth Graphs to Reflexive Graphs: a Complete Complexity Characterization
- MathematicsSTACS
- 2018
This work proves for every fixed non-interval graph H that if a tree decomposition of width tw(G) is given in the input, then the problem can be solved in time i^*(H)^{tw(G)} n^{O(1)}.
Parameterized Graph Modification Algorithms
- Mathematics, Computer Science
- 2015
This thesis shows that editing towards trivially perfect graphs, threshold graphs, and chain graphs are all NP-complete, resolving 15 year old open questions and provides several new results in classical complexity, kernelization complexity, and subexponential parameterized complexity.
Close relatives (of Feedback Vertex Set), revisited
- MathematicsIPEC
- 2021
A common theme of the first two algorithmic results is to represent connectivity properties of the current graph in a state of a dynamic programming algorithm as an auxiliary forest with O(k) nodes, resulting in a 2O(k log k) bound on the number of states for one node of the tree decomposition or cliquewidth expression.
Reducing graph transversals via edge contractions
- MathematicsMFCS
- 2020
This work proves co-NP-hardness results under some assumptions on the graphs in ${\cal H}$, which implies that Contraction ($\pi$) is co- NP-hard even for fixed $k=d=1$ when $\pi$ is the size of a minimum feedback vertex set or an odd cycle transversal.
Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs
- MathematicsAlgorithmica
- 2020
It is proved that the problem of finding a largest, in terms of the number of vertices, induced subgraph of a graph G that belongs to $\mathcal{C}$ can be solved in $2^{o(n)$ time.
Proportionally Fair Matching with Multiple Groups
- Computer ScienceArXiv
- 2023
This work designs exact and approximation algorithms achieving reasonable guarantees on the quality of the matching as well as on the time complexity of proportionally fair matching with more than two groups.
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