scholarly journals The Longest Path Problem has a Polynomial Solution on Interval Graphs

Algorithmica ◽  
2010 ◽  
Vol 61 (2) ◽  
pp. 320-341 ◽  
Author(s):  
Kyriaki Ioannidou ◽  
George B. Mertzios ◽  
Stavros D. Nikolopoulos
Keyword(s):  
Polynomial Solution ◽  
Interval Graphs ◽  
Longest Path ◽  
Longest Path Problem

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

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 Polynomial fixed-parameter algorithms: A case study for longest path on interval graphs

2017 ◽  
Vol 689 ◽  
pp. 67-95 ◽  
Author(s):  
Archontia C. Giannopoulou ◽  
George B. Mertzios ◽  
Rolf Niedermeier
Keyword(s):  
Interval Graphs ◽  
Fixed Parameter ◽  
Longest Path

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

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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