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  Generalized topological sorting in linear time

Hagerup, T., & Maas, M.(1993). Generalized topological sorting in linear time (MPI-I-93-119). Saarbrücken: Max-Planck-Institut für Informatik.

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MPI-I-93-119.pdf (Any fulltext), 7MB
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Hagerup, Torben1, Author           
Maas, Martin1, Author
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1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: The generalized topological sorting problem takes as input a positive integer $k$ and a directed, acyclic graph with some vertices labeled by positive integers, and the goal is to label the remaining vertices by positive integers in such a way that each edge leads from a lower-labeled vertex to a higher-labeled vertex, and such that the set of labels used is exactly $\{1,\ldots,k\}$. Given a generalized topological sorting problem, we want to compute a solution, if one exists, and also to test the uniqueness of a given solution. % The best previous algorithm for the generalized topological sorting problem computes a solution, if one exists, and tests its uniqueness in $O(n\log\log n+m)$ time on input graphs with $n$ vertices and $m$ edges. We describe improved algorithms that solve both problems in linear time $O(n+m)$.

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Language(s): eng - English
 Dates: 1993
 Publication Status: Issued
 Pages: 10 p.
 Publishing info: Saarbrücken : Max-Planck-Institut für Informatik
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 Identifiers: URI: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/93-119
Report Nr.: MPI-I-93-119
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Title: Research Report / Max-Planck-Institut für Informatik
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