scholarly journals A Fixed-Parameter Algorithm for the Max-Cut Problem on Embedded 1-Planar Graphs

2018 ◽  
pp. 141-152 ◽  
Author(s):  
Christine Dahn ◽  
Nils M. Kriege ◽  
Petra Mutzel
Keyword(s):  
Planar Graphs ◽  
Fixed Parameter ◽  
Max Cut Problem ◽  
Fixed Parameter Algorithm

scholarly journals Fixed-parameter algorithms for the weighted Max-Cut problem on embedded 1-planar graphs

2021 ◽  
Vol 852 ◽  
pp. 172-184
Author(s):  
Christine Dahn ◽  
Nils M. Kriege ◽  
Petra Mutzel ◽  
Julian Schilling
Keyword(s):  
Planar Graphs ◽  
Fixed Parameter ◽  
Max Cut Problem

scholarly journals Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs

2003 ◽  
pp. 829-844 ◽  
Author(s):  
Erik D. Demaine ◽  
Fedor V. Fomin ◽  
Mohammad Taghi Hajiaghayi ◽  
Dimitrios M. Thilikos
Keyword(s):  
Planar Graphs ◽  
Fixed Parameter ◽  
Map Graphs

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.

scholarly journals Fixed-parameter algorithms for ( k , r )-center in planar graphs and map graphs

2005 ◽  
Vol 1 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Erik D. Demaine ◽  
Fedor V. Fomin ◽  
Mohammadtaghi Hajiaghayi ◽  
Dimitrios M. Thilikos
Keyword(s):  
Planar Graphs ◽  
Fixed Parameter ◽  
Map Graphs

A fixed-parameter algorithm for the maximum agreement forest problem on multifurcating trees

2015 ◽  
Vol 59 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Feng Shi ◽  
Jianxin Wang ◽  
Yufei Yang ◽  
Qilong Feng ◽  
Weilong Li ◽  
...  
Keyword(s):  
Maximum Agreement Forest ◽  
Fixed Parameter ◽  
Fixed Parameter Algorithm

Fixed Parameter Algorithms for DOMINATING SET and Related Problems on Planar Graphs

Algorithmica ◽  
2002 ◽  
Vol 33 (4) ◽  
pp. 461-493 ◽  
Author(s):  
J. Alber ◽  
H. L. Bodlaender ◽  
H. Fernau ◽  
T. Kloks ◽  
R. Niedermeier
Keyword(s):  
Planar Graphs ◽  
Dominating Set ◽  
Fixed Parameter

An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number

2019 ◽  
pp. 327-338
Author(s):  
Yasuaki Kobayashi ◽  
Yusuke Kobayashi ◽  
Shuichi Miyazaki ◽  
Suguru Tamaki
Keyword(s):  
Crossing Number ◽  
Fixed Parameter ◽  
Fixed Parameter Algorithm

scholarly journals A fixed-parameter algorithm for guarding 1.5D terrains

2015 ◽  
Vol 595 ◽  
pp. 130-142 ◽  
Author(s):  
Farnoosh Khodakarami ◽  
Farzad Didehvar ◽  
Ali Mohades
Keyword(s):  
Fixed Parameter ◽  
Fixed Parameter Algorithm
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