The Longest Path Problem has a Polynomial Solution on Interval Graphs
نویسندگان
چکیده
منابع مشابه
The Longest Path Problem Is Polynomial on Interval Graphs
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, ...
متن کاملA polynomial solution to the k-fixed-endpoint path cover problem on proper interval graphs
We study a variant of the path cover problem, namely, the k-fixed-endpoint path cover problem, or kPC for short. Given a graph G and a subset T of k vertices of V (G), a k-fixed-endpoint path cover of G with respect to T is a set of vertex-disjoint paths P that covers the vertices of G such that the k vertices of T are all endpoints of the paths in P. The kPC problem is to find a k-fixed-endpoi...
متن کاملThe Longest Path Problem on Permutation Graphs
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 کاملPolynomial Fixed-parameter Algorithms: A Case Study for Longest Path on Interval Graphs
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...
متن کاملA 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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algorithmica
سال: 2010
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-010-9411-3