A Linear Time Algorithm for the 1-Fixed-Endpoint Path Cover Problem on Interval Graphs

2017 ◽  
Vol 31 (1) ◽  
pp. 210-239 ◽  
Author(s):  
Peng Li ◽  
Yaokun Wu
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Interval Graphs ◽  
Linear Time Algorithm ◽  
Path Cover ◽  
Cover Problem

A linear-time algorithm for thek-fixed-endpoint path cover problem on cographs

Networks ◽  
2007 ◽  
Vol 50 (4) ◽  
pp. 231-240 ◽  
Author(s):  
Katerina Asdre ◽  
Stavros D. Nikolopoulos
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Path Cover ◽  
Cover Problem

scholarly journals Computing directed Steiner path covers

2021 ◽  
Author(s):  
Frank Gurski ◽  
Dominique Komander ◽  
Carolin Rehs ◽  
Jochen Rethmann ◽  
Egon Wanke
Keyword(s):  
Linear Time ◽  
Hamiltonian Path ◽  
Time Algorithm ◽  
Integer Programs ◽  
Path Cover ◽  
Hamiltonian Path Problem ◽  
Directed Paths ◽  
Minimum Number ◽  
Cover Problem ◽  
Vertex Disjoint

AbstractIn this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a directed graph $$G=(V,E)$$ G = ( V , E ) and a set $$T \subseteq V$$ T ⊆ V of so-called terminal vertices, the problem is to find a minimum number of vertex-disjoint simple directed paths, which contain all terminal vertices and a minimum number of non-terminal vertices (Steiner vertices). The primary minimization criteria is the number of paths. We show how to compute in linear time a minimum Steiner path cover for directed co-graphs. This leads to a linear time computation of an optimal directed Steiner path on directed co-graphs, if it exists. Since the Steiner path problem generalizes the Hamiltonian path problem, our results imply the first linear time algorithm for the directed Hamiltonian path problem on directed co-graphs. We also give binary integer programs for the (directed) Hamiltonian path problem, for the (directed) Steiner path problem, and for the (directed) Steiner path cover problem. These integer programs can be used to minimize change-over times in pick-and-place machines used by companies in electronic industry.

An Incremental Linear-Time Algorithm for Recognizing Interval Graphs

1989 ◽  
Vol 18 (1) ◽  
pp. 68-81 ◽  
Author(s):  
Norbert Korte ◽  
Rolf H. Möhring
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Interval Graphs ◽  
Linear Time Algorithm
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