Parameterized Algorithmics for Finding Exact Solutions of NP-Hard Biological Problems

2016 ◽  
pp. 363-402 ◽  
Author(s):  
Falk Hüffner ◽  
Christian Komusiewicz ◽  
Rolf Niedermeier ◽  
Sebastian Wernicke
Keyword(s):  
Exact Solutions ◽  
Np Hard ◽  
Parameterized Algorithmics

scholarly journals A Parameterized Measure-and-ConquerAnalysis for Finding a k-Leaf Spanning Treein an Undirected Graph

2014 ◽  
Vol Vol. 16 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Daniel Binkele-Raible ◽  
Henning Fernau
Keyword(s):  
Spanning Tree ◽  
Undirected Graph ◽  
Standard Measure ◽  
Algorithm Analysis ◽  
Np Hard ◽  
Running Time ◽  
Discrete Algorithms ◽  
Parameterized Algorithmics ◽  
International Audience ◽  
Number Of Leaves

Discrete Algorithms International audience The problem of finding a spanning tree in an undirected graph with a maximum number of leaves is known to be NP-hard. We present an algorithm which finds a spanning tree with at least k leaves in time O*(3.4575k) which improves the currently best algorithm. The estimation of the running time is done by using a non-standard measure. The present paper is one of the still few examples that employ the Measure & Conquer paradigm of algorithm analysis in the area of Parameterized Algorithmics.

scholarly journals Faster exact solutions for some NP-hard problems

2002 ◽  
Vol 287 (2) ◽  
pp. 473-499 ◽  
Author(s):  
Limor Drori ◽  
David Peleg
Keyword(s):  
Exact Solutions ◽  
Np Hard ◽  
Hard Problems ◽  
Np Hard Problems

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

Sign in / Sign up

Export Citation Format

Share Document