Algorithms for long paths in graphs
Zhao Zhang,Hao Li +1 more
TLDR
A polynomial algorithm in O(nm) time to find a long path in any graph with n vertices and m edges is obtained, bounded by a parameter defined on neighborhood condition of any three independent vertices of the path.About:
This article is published in Theoretical Computer Science.The article was published on 2007-05-25 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Path graph & Longest path problem.read more
Citations
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The Longest Path Problem Is Polynomial on Interval Graphs
TL;DR: The longest path problem is shown to be solved in polynomial time on interval graphs, and the proposed algorithm runs in O(n 4) time, where n is the number of vertices of the input graph, and bases on a dynamic programming approach.
Journal ArticleDOI
The Longest Path Problem has a Polynomial Solution on Interval Graphs
TL;DR: The longest path problem can be solved in polynomial time on interval graphs with a dynamic programming approach and runs in O(n4) time, where n is the number of vertices of the input graph.
Journal ArticleDOI
A linear-time algorithm for the longest path problem in rectangular grid graphs
TL;DR: This paper gives a linear-time algorithm for finding a longest path between any two given vertices in a rectangular grid graph.
Journal ArticleDOI
The Longest Path Problem Is Polynomial on Cocomparability Graphs
TL;DR: The result resolves the open question for the complexity of the problem on such graphs, and since cocomparability graphs form a superclass of both interval and permutation graphs, extends the polynomial solution of the longest path problem on interval graphs and provides polynometric solution to the class of permutations graphs.
Journal ArticleDOI
An efficient parallel algorithm for the longest path problem in meshes
TL;DR: First a sequential linear-time algorithm for the longest path problem in meshes is given, and based on this algorithm a constant-time parallel algorithm is presented, which can be run on every parallel machine.
References
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Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Journal ArticleDOI
Graph theory with applications (revised edition), by J. A. Bondy and U.S.R. Murty. Pp x, 264. £5·95 paperback. 1977. SBN 0 333 22694 1 (Macmillan)
Book
Combinatorial Optimization: Theory and Algorithms
Bernhard Korte,Jens Vygen +1 more
TL;DR: This fourth edition of this comprehensive textbook on combinatorial optimization is again significantly extended, most notably with new material on linear programming, the network simplex algorithm, and the max-cut problem.