# On the complexity of various parameterizations of common induced subgraph isomorphism

@inproceedings{AbuKhzam2014OnTC, title={On the complexity of various parameterizations of common induced subgraph isomorphism}, author={Faisal N. Abu-Khzam and {\'E}douard Bonnet and Florian Sikora}, booktitle={Theor. Comput. Sci.}, year={2014} }

## 5 Citations

### Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters

- Mathematics, Computer ScienceOPODIS
- 2021

This work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph, and shows that induced paths can be detected fast in CONGEST using techniques from parameterization algorithms, while detecting cycles and patterns of treewidth 2 is hard.

### Streaming Deletion Problems Parameterized by Vertex Cover

- Computer ScienceFCT
- 2021

This work takes a parameterized approach by assuming a vertex cover of the graph is given, building on work of Bishnu et al.

### Improved Hardness of Maximum Common Subgraph Problems on Labeled Graphs of Bounded Treewidth and Bounded Degree

- MathematicsInt. J. Found. Comput. Sci.
- 2020

This work considers the maximum common connected edge subgraph problem and themaximum common connected induced sub graph problem for simple graphs with labeled vertices (or labeled edges) and concludes that the former is to be solved and the latter is not.

### A genetic approach to the maximum common subgraph problem

- Computer ScienceCompSysTech
- 2019

A simple yet effective genetic algorithm that finds quickly a solution, subject to possible geometric constraints, in the problem of finding the maximum common subgraph of a pair of given graphs.

### Chemical Similarity and Substructure Searches

- Computer ScienceEncyclopedia of Bioinformatics and Computational Biology
- 2019

## References

SHOWING 1-10 OF 37 REFERENCES

### Maximum common induced subgraph parameterized by vertex cover

- Mathematics, Computer ScienceInf. Process. Lett.
- 2014

### Short Cycles Make W-hard Problems Hard: FPT Algorithms for W-hard Problems in Graphs with no Short Cycles

- Mathematics, Computer ScienceAlgorithmica
- 2007

Abstract
We show that several problems that are hard for various parameterized complexity classes on general graphs, become fixed parameter tractable on graphs with no small cycles.
More…

### Induced Subgraph Isomorphism on proper interval and bipartite permutation graphs

- MathematicsTheor. Comput. Sci.
- 2015

### Linear Time Algorithms for Finding a Dominating Set of Fixed Size in Degenerated Graphs

- MathematicsAlgorithmica
- 2008

This paper gives a kO(dk)n time algorithm for finding a dominating set of size at most k in a d-degenerated graph with n vertices, which proves that the dominating set problem is fixed-parameter tractable for degenerated graphs.

### Cleaning Interval Graphs

- MathematicsAlgorithmica
- 2011

The NP-hardness of the Induced Subgraph Isomorphism problem is shown, and fixed-parameter tractability of the problem with non-standard parameterization is proved, where the parameter is the difference |V(G)|−|V(H)|.

### Deciding first-order properties of nowhere dense graphs

- Mathematics, Computer ScienceSTOC
- 2014

It is shown that deciding properties of graphs definable in first-order logic is fixed-parameter tractable on nowhere dense graph classes, and a "rank-preserving" version of Gaifman's locality theorem is proved.

### Algorithmic Aspects of Dominator Colorings in Graphs

- MathematicsIWOCA
- 2011

It is shown that unless P=NP, DC cannot be solved in polynomial time on bipartite, planar, or split graphs and that the problem is fixed parameter tractable (FPT) on chordal graphs and in graphs which exclude a fixed apex graph as a minor.

### Random Separation: A New Method for Solving Fixed-Cardinality Optimization Problems

- MathematicsIWPEC
- 2006

A new randomized method, random separation, for solving fixed-cardinality optimization problems on graphs, i.e., problems concerning solutions with exactly a fixed number k of elements that optimize solution values is developed.

### Finding the Maximum Common Subgraph of a Partial k-Tree and a Graph with a Polynomially Bounded Number of Spanning Trees

- MathematicsISAAC
- 2003

A polynomial time algorithm is presented for finding the maximum common connected induced subgraph of a degree-bounded partial k-tree and a connected graph, the number of whose possible spanning trees isPolynomial.