MPI-INF/SWS Research Reports 1991-2021

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Generalized topological sorting in linear time

Hagerup, Torben and Maas, Martin

May 1993, 10 pages.

Status: available - back from printing

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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  AUTHOR = {Hagerup, Torben and Maas, Martin},
  TITLE = {Generalized topological sorting in linear time},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-93-119},
  MONTH = {May},
  YEAR = {1993},
  ISSN = {0946-011X},