scholarly journals A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees

2013 ◽  
Vol 10 (1) ◽  
pp. 18-25 ◽  
Author(s):  
Teresa Piovesan ◽  
Steven M. Kelk
Keyword(s):  
Binary Trees ◽  
Fixed Parameter Tractable ◽  
Fixed Parameter ◽  
Hybridization Number

scholarly journals Towards fixed-parameter tractable algorithms for abstract argumentation

2012 ◽  
Vol 186 ◽  
pp. 1-37 ◽  
Author(s):  
Wolfgang Dvořák ◽  
Reinhard Pichler ◽  
Stefan Woltran
Keyword(s):  
Fixed Parameter Tractable ◽  
Abstract Argumentation ◽  
Fixed Parameter

scholarly journals Interval Completion Is Fixed Parameter Tractable

2009 ◽  
Vol 38 (5) ◽  
pp. 2007-2020 ◽  
Author(s):  
Yngve Villanger ◽  
Pinar Heggernes ◽  
Christophe Paul ◽  
Jan Arne Telle
Keyword(s):  
Fixed Parameter Tractable ◽  
Fixed Parameter

When is Red-Blue Nonblocker Fixed-Parameter Tractable?

2018 ◽  
pp. 515-528
Author(s):  
Serge Gaspers ◽  
Joachim Gudmundsson ◽  
Michael Horton ◽  
Stefan Rümmele
Keyword(s):  
Fixed Parameter Tractable ◽  
Fixed Parameter

scholarly journals Threshold Treewidth and Hypertree Width

2020 ◽  
Author(s):  
Robert Ganian ◽  
Andre Schidler ◽  
Manuel Sorge ◽  
Stefan Szeider
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Structural Parameters ◽  
Exact Methods ◽  
Fixed Parameter Tractable ◽  
Computational Costs ◽  
Fixed Parameter ◽  
Account Information ◽  
The Given ◽  
Theoretical Results

Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in polynomial time. However, here the order of the polynomial in the running time depends on the width, and this is known to be unavoidable; therefore, the problem is not fixed-parameter tractable parameterized by either of these width measures. Here we introduce an enhancement of tree and hypertree width through a novel notion of thresholds, allowing the associated decompositions to take into account information about the computational costs associated with solving the given CSP instance. Aside from introducing these notions, we obtain efficient theoretical as well as empirical algorithms for computing threshold treewidth and hypertree width and show that these parameters give rise to fixed-parameter algorithms for CSP as well as other, more general problems. We complement our theoretical results with experimental evaluations in terms of heuristics as well as exact methods based on SAT/SMT encodings.

Multiplicative Parameterization Above a Guarantee

2021 ◽  
Vol 13 (3) ◽  
pp. 1-16
Author(s):  
Fedor V. Fomin ◽  
Petr A. Golovach ◽  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh ◽  
...  
Keyword(s):  
Minimum Size ◽  
Input Graph ◽  
Fixed Parameter Tractable ◽  
Long Cycle ◽  
Fixed Parameter ◽  
Parameterized Problem ◽  
Fixed Constant ◽  
Fixed Parameter Algorithm ◽  
Np Hardness ◽  
Additive Form

Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given an instance ( I,k ) of some (parameterized) problem π with a guarantee g(I) , decide whether I admits a solution of size at least (or at most) k + g(I) . Here, g(I) is usually a lower bound on the minimum size of a solution. Since its introduction in 1999 for M AX SAT and M AX C UT (with g(I) being half the number of clauses and half the number of edges, respectively, in the input), analysis of parameterization above a guarantee has become a very active and fruitful topic of research. We highlight a multiplicative form of parameterization above (or, rather, times) a guarantee: Given an instance ( I,k ) of some (parameterized) problem π with a guarantee g(I) , decide whether I admits a solution of size at least (or at most) k · g(I) . In particular, we study the Long Cycle problem with a multiplicative parameterization above the girth g(I) of the input graph, which is the most natural guarantee for this problem, and provide a fixed-parameter algorithm. Apart from being of independent interest, this exemplifies how parameterization above a multiplicative guarantee can arise naturally. We also show that, for any fixed constant ε > 0, multiplicative parameterization above g(I) 1+ε of Long Cycle yields para-NP-hardness, thus our parameterization is tight in this sense. We complement our main result with the design (or refutation of the existence) of fixed-parameter algorithms as well as kernelization algorithms for additional problems parameterized multiplicatively above girth.

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