Parameterized Complexity of the Sparsest k-Subgraph Problem in Chordal Graphs

2014 ◽  
pp. 150-161 ◽  
Author(s):  
Marin Bougeret ◽  
Nicolas Bousquet ◽  
Rodolphe Giroudeau ◽  
Rémi Watrigant
Keyword(s):  
Parameterized Complexity ◽  
Chordal Graphs

scholarly journals On the Parameterized Approximability of Contraction to Classes of Chordal Graphs

2021 ◽  
Vol 13 (4) ◽  
pp. 1-40
Author(s):  
Spoorthy Gunda ◽  
Pallavi Jain ◽  
Daniel Lokshtanov ◽  
Saket Saurabh ◽  
Prafullkumar Tale
Keyword(s):  
Approximation Algorithm ◽  
Arbitrary Function ◽  
Parameterized Complexity ◽  
Chordal Graphs ◽  
Polynomial Kernel ◽  
Graph Minors ◽  
Polynomial Size ◽  
Graph Operation ◽  
Approximate Polynomial ◽  
Scientific Attention

A graph operation that contracts edges is one of the fundamental operations in the theory of graph minors. Parameterized Complexity of editing to a family of graphs by contracting k edges has recently gained substantial scientific attention, and several new results have been obtained. Some important families of graphs, namely, the subfamilies of chordal graphs, in the context of edge contractions, have proven to be significantly difficult than one might expect. In this article, we study the F -Contraction problem, where F is a subfamily of chordal graphs, in the realm of parameterized approximation. Formally, given a graph G and an integer k , F -Contraction asks whether there exists X ⊆ E(G) such that G/X ∈ F and | X | ≤ k . Here, G/X is the graph obtained from G by contracting edges in X . We obtain the following results for the F - Contraction problem: • Clique Contraction is known to be FPT . However, unless NP⊆ coNP/ poly , it does not admit a polynomial kernel. We show that it admits a polynomial-size approximate kernelization scheme ( PSAKS ). That is, it admits a (1 + ε)-approximate kernel with O ( k f(ε)) vertices for every ε > 0. • Split Contraction is known to be W[1]-Hard . We deconstruct this intractability result in two ways. First, we give a (2+ε)-approximate polynomial kernel for Split Contraction (which also implies a factor (2+ε)- FPT -approximation algorithm for Split Contraction ). Furthermore, we show that, assuming Gap-ETH , there is no (5/4-δ)- FPT -approximation algorithm for Split Contraction . Here, ε, δ > 0 are fixed constants. • Chordal Contraction is known to be W[2]-Hard . We complement this result by observing that the existing W[2]-hardness reduction can be adapted to show that, assuming FPT ≠ W[1] , there is no F(k) - FPT -approximation algorithm for Chordal Contraction . Here, F(k) is an arbitrary function depending on k alone. We say that an algorithm is an h(k) - FPT -approximation algorithm for the F -Contraction problem, if it runs in FPT time, and on any input (G, k) such that there exists X ⊆ E(G) satisfying G/X ∈ F and | X | ≤ k , it outputs an edge set Y of size at most h(k) ċ k for which G/Y is in F .

On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances

2017 ◽  
Vol 18 (3) ◽  
pp. 1-46
Author(s):  
Ronald De Haan ◽  
Iyad Kanj ◽  
Stefan Szeider
Keyword(s):  
Parameterized Complexity ◽  
Cnf Formulas

Parameterized complexity of fair feedback vertex set problem

2021 ◽  
Vol 867 ◽  
pp. 1-12
Author(s):  
Lawqueen Kanesh ◽  
Soumen Maity ◽  
Komal Muluk ◽  
Saket Saurabh
Keyword(s):  
Parameterized Complexity ◽  
Feedback Vertex Set ◽  
Vertex Set ◽  
Feedback Vertex Set Problem

A compendium of parameterized complexity results

1994 ◽  
Vol 25 (3) ◽  
pp. 122-123 ◽  
Author(s):  
Michael T. Hallett ◽  
H. Todd Wareham
Keyword(s):  
Parameterized Complexity ◽  
Complexity Results

scholarly journals Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

2020 ◽  
Vol 847 ◽  
pp. 27-38
Author(s):  
Christian Komusiewicz ◽  
Mateus de Oliveira Oliveira ◽  
Meirav Zehavi
Keyword(s):  
Parameterized Complexity

The Book Review Column1

2021 ◽  
Vol 51 (4) ◽  
pp. 4-5
Author(s):  
Frederic Green
Keyword(s):  
Parameterized Complexity ◽  
Property Testing ◽  
The Third ◽  
Geometric Problems ◽  
The Subject

The three books reviewed in this column are about central ideas in algorithms, complexity, and geometry. The third one brings together topics from the first two by applying techniques of both property testing (the subject of the first book) and parameterized complexity (including its more focused incarnation studied in the second book, kernelization) to geometric problems.

Chordal graphs

2021 ◽  
pp. 130-151
Author(s):  
Martin Charles Golumbic
Keyword(s):  
Chordal Graphs

On 3-Degree 4-Chordal Graphs

2020 ◽  
Author(s):  
Devarshi Aggarwal ◽  
R.Mahendra Kumar ◽  
Shwet Prakash ◽  
N. Sadagopan
Keyword(s):  
Chordal Graphs

scholarly journals Parameterized complexity for the database theorist

2002 ◽  
Vol 31 (4) ◽  
pp. 86-96 ◽  
Author(s):  
Martin Grohe
Keyword(s):  
Parameterized Complexity
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