Algebraic tools for the construction of colored flows with boundary constraints
Marius Dorkenoo; Marie-Christine Eglin-Leclerc; Eric Rémila
RAIRO - Theoretical Informatics and Applications (2010)
- Volume: 38, Issue: 3, page 229-243
- ISSN: 0988-3754
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topDorkenoo, Marius, Eglin-Leclerc, Marie-Christine, and Rémila, Eric. "Algebraic tools for the construction of colored flows with boundary constraints." RAIRO - Theoretical Informatics and Applications 38.3 (2010): 229-243. <http://eudml.org/doc/92740>.
@article{Dorkenoo2010,
abstract = {
We give a linear time algorithm which, given a simply connected
figure of the plane
divided into cells, whose boundary is crossed by some colored inputs
and outputs,
produces non-intersecting directed flow lines which match inputs and
outputs according
to the colors, in such a way that each edge of any cell is crossed by
at most one line. The main tool is the notion of height function,
previously introduced for tilings. It appears as an
extension of the notion of potential of a flow in a planar graph.
},
author = {Dorkenoo, Marius, Eglin-Leclerc, Marie-Christine, Rémila, Eric},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Height function; planar flows; planar graphs; flow; multicommodity flow},
language = {eng},
month = {3},
number = {3},
pages = {229-243},
publisher = {EDP Sciences},
title = {Algebraic tools for the construction of colored flows with boundary constraints},
url = {http://eudml.org/doc/92740},
volume = {38},
year = {2010},
}
TY - JOUR
AU - Dorkenoo, Marius
AU - Eglin-Leclerc, Marie-Christine
AU - Rémila, Eric
TI - Algebraic tools for the construction of colored flows with boundary constraints
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 3
SP - 229
EP - 243
AB -
We give a linear time algorithm which, given a simply connected
figure of the plane
divided into cells, whose boundary is crossed by some colored inputs
and outputs,
produces non-intersecting directed flow lines which match inputs and
outputs according
to the colors, in such a way that each edge of any cell is crossed by
at most one line. The main tool is the notion of height function,
previously introduced for tilings. It appears as an
extension of the notion of potential of a flow in a planar graph.
LA - eng
KW - Height function; planar flows; planar graphs; flow; multicommodity flow
UR - http://eudml.org/doc/92740
ER -
References
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- W.P. Thurston, Conway's tiling group. Amer. Math. Monthly (1990) 757–773.
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