scholarly journals Towards a Fixed Parameter Tractability of Geometric Hitting Set Problem for Axis-Parallel Squares Intersecting a Given Straight Line

2017 ◽  
Author(s):  
Daniel KHACHAY ◽  
Michael KHACHAY ◽  
Maria POBERIY
Keyword(s):  
Fixed Parameter Tractability ◽  
Hitting Set ◽  
Straight Line ◽  
Fixed Parameter ◽  
Axis Parallel ◽  
Hitting Set Problem

THE COMPUTATIONAL COMPLEXITY OF AVOIDING FORBIDDEN SUBMATRICES BY ROW DELETIONS

2006 ◽  
Vol 17 (06) ◽  
pp. 1467-1484 ◽  
Author(s):  
SEBASTIAN WERNICKE ◽  
JOCHEN ALBER ◽  
JENS GRAMM ◽  
JIONG GUO ◽  
ROLF NIEDERMEIER
Keyword(s):  
Close Relation ◽  
Constant Factor ◽  
Input Matrix ◽  
Hitting Set ◽  
Positive Side ◽  
Column Permutation ◽  
Fixed Parameter ◽  
Minimum Number ◽  
Np Complete ◽  
Hitting Set Problem

We initiate a systematic study of the ROW DELETION(B) problem on matrices: Given an input matrix A and a fixed "forbidden submatrix" B, the task is to remove a minimum number of rows from A such that no row or column permutation of B occurs as a submatrix in the resulting matrix. An application of this problem can be found, for instance, in the construction of perfect phylogenies. Establishing a strong connection to variants of the NP-complete HITTING SET problem, we describe and analyze structural properties of B that make ROW DELETION(B)NP-complete. On the positive side, the close relation with HITTING SET problems yields constant-factor polynomial-time approximation algorithms and fixed-parameter tractability results.

scholarly journals Fixed-parameter tractability and lower bounds for stabbing problems

2013 ◽  
Vol 46 (7) ◽  
pp. 839-860 ◽  
Author(s):  
Panos Giannopoulos ◽  
Christian Knauer ◽  
Günter Rote ◽  
Daniel Werner
Keyword(s):  
Lower Bounds ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

Fixed-parameter tractability for the tree assembly problem

2021 ◽  
Author(s):  
Feng Shi ◽  
Jie You ◽  
Zhen Zhang ◽  
Jingyi Liu ◽  
Jianxin Wang
Keyword(s):  
Fixed Parameter Tractability ◽  
Fixed Parameter ◽  
Assembly Problem

Fixed-parameter tractability and data reduction for multicut in trees

Networks ◽  
2005 ◽  
Vol 46 (3) ◽  
pp. 124-135 ◽  
Author(s):  
Jiong Guo ◽  
Rolf Niedermeier
Keyword(s):  
Data Reduction ◽  
Fixed Parameter Tractability ◽  
Fixed Parameter

scholarly journals Fixed-Parameter Tractability of Satisfying Beyond the Number of Variables

Algorithmica ◽  
2012 ◽  
Vol 68 (3) ◽  
pp. 739-757 ◽  
Author(s):  
Robert Crowston ◽  
Gregory Gutin ◽  
Mark Jones ◽  
Venkatesh Raman ◽  
Saket Saurabh ◽  
...  
Keyword(s):  
Fixed Parameter Tractability ◽  
Fixed Parameter

scholarly journals Finding Points in General Position

2017 ◽  
Vol 27 (04) ◽  
pp. 277-296 ◽  
Author(s):  
Vincent Froese ◽  
Iyad Kanj ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Lower Bound ◽  
General Position ◽  
Subset Selection ◽  
Selection Problem ◽  
Fixed Parameter Tractability ◽  
Maximum Cardinality ◽  
Exponential Time ◽  
Running Time ◽  
Fixed Parameter ◽  
Set Of Points

We study the General Position Subset Selection problem: Given a set of points in the plane, find a maximum-cardinality subset of points in general position. We prove that General Position Subset Selection is NP-hard, APX-hard, and present several fixed-parameter tractability results for the problem as well as a subexponential running time lower bound based on the Exponential Time Hypothesis.

ON NONLINEAR WAVE EQUATIONS WITH BREAKING LOOP-SOLUTIONS

2010 ◽  
Vol 20 (02) ◽  
pp. 519-537 ◽  
Author(s):  
JIBIN LI ◽  
GUANRONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Nonlinear Wave ◽  
Traveling Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Level Curves ◽  
Straight Line ◽  
Fixed Parameter ◽  
Unstable Manifolds

Using analytic methods from the dynamical systems theory, some new nonlinear wave equations are investigated, which have exact explicit parametric representations of breaking loop-solutions under some fixed parameter conditions. It is shown that these parametric representations are associated with some families of open level-curves of traveling wave systems corresponding to such nonlinear wave equations, each of which lies in an area bounded by a singular straight line and the stable and the unstable manifolds of a saddle point of such a system.

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