The Longest Path Problem Is Polynomial on Cocomparability Graphs
نویسندگان
چکیده
منابع مشابه
A Simple Polynomial Algorithm for the Longest Path Problem on Cocomparability Graphs
Given a graph G, the longest path problem asks to compute a simple path of G with the largest number of vertices. This problem is the most natural optimization version of the well-known and well-studied Hamiltonian path problem, and thus it is NP-hard on general graphs. However, in contrast to the Hamiltonian path problem, there are only a few restricted graph families, such as trees, and some ...
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The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamiltonian path problem. Motivated by the work of Uehara and Uno in [22], where they left the longest path problem open for the class of interval graphs, ...
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The longest path problem on graph G is a classic problem which is to find a simple path such that the number of vertices of the path is maximum among all possible paths of G. In this paper, we show that the longest path problem can be solved in linear time on permutation graphs.
متن کاملLongest Path Problems on Ptolemaic Graphs
SUMMARY Longest path problem is a problem for finding a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, there are few known graph classes such that the longest path problem can be solved efficiently. Polynomial time algorithms for finding a longest cycle and a longest path in a Ptolemaic graph are pr...
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We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus on a fundamental graph problem: Longest Path, that is, given an undirected graph, find a maximum-length path in G. Longest Path is NP-hard in general but kno...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2011
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-011-9583-5