#11736: Linear time implementation of lex_BFS()
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Reporter: ddestrada | Owner: jason, ncohen, rlm
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-4.7.2
Component: graph theory | Keywords: lexbfs
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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The current implementation of lex_BFS() is quadratic, which is not
optimal. The usual way to do it in linear time is through a clever use of
doubly linked lists, but in [1] there is a way with static arrays, which I
coded in Python.
There is one thing, though: in [2] there is a new algorithm for
is_interval() that avoids PQ-trees, and just uses various passes of
lex_BFS() (implemented with doubly linked lists).
So maybe in the long run it would be better to do it with doubly linked
lists in Cython.
[1] Habib, McConnell, Paul and Viennot. Lex-BFS and Partition Refinement,
with Applications to Transitive Orientation, Interval Graph Recognition
and Consecutive Ones Testing. TCS 234, 2000.
[2] Corneil, Olariu and Stewart. The LBFS Structure and Recognition of
Interval Graphs. SIAMDM 23(4), 2009.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11736>
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