# 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

## Access Full Article

top## Abstract

top## How to cite

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

top- T. Chaboud, Pavages et Graphes de Cayley. Ph.D. Thesis, École Normale Supérieure de Lyon (1995).
- J.H. Conway and J.C. Lagarias, Tiling with Polyominoes and Combinatorial Group Theory. J. Combin. Theory A53 (1990) 183–208. Zbl0741.05019
- R. Hassin, Maximum flows in (s,t) planar networks. Inform. Proc. Lett.13 (1981) 107.
- R. Hassin and D.B. Johnson, An O(nlog²n) algorithm for maximum flow in undirected planar networks. SIAM J. Comput.14 (1985) 612–624. Zbl0565.90018
- C. Kenyon and R. Kenyon, Tiling a polygon with rectangles. Proc. 33rd FOCS (1992) 610–619. Zbl0915.05039
- J. Kondev and Ch.L. Henley, Kac-Moody symmetries of critical ground states. Nuclear Phys. B464 (1996) 540–575. Zbl1004.82501
- J.C. Lagarias and D.S. Romano, A Polyomino Tiling of Thurston and its Configurational Entropy. J. Combin. Theory A63 (1993) 338–358. Zbl0777.52013
- W. Magnus, A. Karass and D. Solitar, Combinatorial Group Theory. Dover Publications, Inc. (1976).
- J. Propp, A pedestrian approach to a method of Conway, or a tale of two cities. Internal Report, Massachusetts Institute of Technology (1993). Zbl0897.05022
- E. Rémila, Tiling a figure using a height in a tree, in Proc. of the 7th annual ACM-SIAM Symposium On Discrete Algorithms (SODA). SIAM eds, Philadelphia (1996) 168–174. Zbl0848.68046
- W.P. Thurston, Conway's tiling group. Amer. Math. Monthly (1990) 757–773. Zbl0714.52007

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.