MPI-I-93-119
Generalized topological sorting in linear time
Hagerup, Torben and Maas, Martin
May 1993, 10 pages.
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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 $O(n+m)$.
URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1993-119
BibTeX
@TECHREPORT{HagerupMaas93,
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},
}