scholarly journals A SPECIAL CASE OF LONGEST PATH PROBLEM

2018 ◽  
Author(s):  
Thinh D. Nguyen
Keyword(s):  
Hamiltonian Path ◽  
Longest Path ◽  
Longest Path Problem ◽  
Special Case

We have that Hamiltonian Path can be reduced to a special case of Longest Path Problem.

scholarly journals ON COMPUTING LONGEST PATHS IN SMALL GRAPH CLASSES

2007 ◽  
Vol 18 (05) ◽  
pp. 911-930 ◽  
Author(s):  
RYUHEI UEHARA ◽  
YUSHI UNO
Keyword(s):  
Linear Time ◽  
Hamiltonian Path ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Graph Classes ◽  
Longest Path ◽  
Longest Path Problem ◽  
Longest Paths ◽  
Interval Representations ◽  
The One

The longest path problem is the one that finds a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, few graph classes are known to be solved efficiently for the longest path problem. Among those, for trees, a simple linear time algorithm for the longest path problem is known. We first generalize the algorithm, and show that the longest path problem can be solved efficiently for some tree-like graph classes by this approach. We next propose two new graph classes that have natural interval representations, and show that the longest path problem can be solved efficiently on these classes.

scholarly journals A linear-time algorithm for the longest path problem in rectangular grid graphs

2012 ◽  
Vol 160 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Fatemeh Keshavarz-Kohjerdi ◽  
Alireza Bagheri ◽  
Asghar Asgharian-Sardroud
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Rectangular Grid ◽  
Grid Graphs ◽  
Longest Path ◽  
Longest Path Problem

scholarly journals The Longest Path Problem Is Polynomial on Cocomparability Graphs

Algorithmica ◽  
2011 ◽  
Vol 65 (1) ◽  
pp. 177-205 ◽  
Author(s):  
Kyriaki Ioannidou ◽  
Stavros D. Nikolopoulos
Keyword(s):  
Longest Path ◽  
Longest Path Problem ◽  
Cocomparability Graphs

scholarly journals The Longest Path Problem Is Polynomial on Interval Graphs

2009 ◽  
pp. 403-414 ◽  
Author(s):  
Kyriaki Ioannidou ◽  
George B. Mertzios ◽  
Stavros D. Nikolopoulos
Keyword(s):  
Interval Graphs ◽  
Longest Path ◽  
Longest Path Problem

Solving the Longest Path Problem Using a Biologically DNA Computational Model

2015 ◽  
Vol 12 (6) ◽  
pp. 1096-1099
Author(s):  
Kai Zhao ◽  
Jun Pu ◽  
Zhaocai Wang ◽  
Huajun Meng
Keyword(s):  
Computational Model ◽  
Longest Path ◽  
Longest Path Problem

scholarly journals Letter to the Editor—Some Observations on the Longest Path Problem

1964 ◽  
Vol 12 (2) ◽  
pp. 361-364 ◽  
Author(s):  
S. N. Narahari Pandit
Keyword(s):  
Letter To The Editor ◽  
Longest Path ◽  
Longest Path Problem

The probabilistic longest path problem

Networks ◽  
1999 ◽  
Vol 33 (3) ◽  
pp. 207-219 ◽  
Author(s):  
C�cile Murat ◽  
Vangelis Th. Paschos
Keyword(s):  
Longest Path ◽  
Longest Path Problem

scholarly journals On the Performance of a Simple Approximation Algorithm for the Longest Path Problem

2019 ◽  
Vol 35 (1) ◽  
pp. 57-68
Author(s):  
Nguyen Thi Phuong ◽  
Tran Vinh Duc ◽  
Le Cong Thanh
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Polynomial Time ◽  
Undirected Graph ◽  
Simple Algorithm ◽  
Performance Ratio ◽  
Constant Ratio ◽  
Time Approximation ◽  
Longest Path ◽  
Longest Path Problem

The longest path problem is known to be NP-hard. Moreover, they cannot be approximated within a constant ratio, unless ${\rm P=NP}$. The best known polynomial time approximation algorithms for this problem essentially find a path of length that is the logarithm of the optimum.In this paper we investigate the performance of an approximation algorithm for this problem in almost every case. We show that a simple algorithm, based on depth-first search, finds on almost every undirected graph $G=(V,E)$ a path of length more than $|V|-3\sqrt{|V| \log |V|}$ and so has performance ratio less than $1+4\sqrt{\log |V|/|V|}$.\

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