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

Abstract

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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.

How to cite

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Dorkenoo, 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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  5. C. Kenyon and R. Kenyon, Tiling a polygon with rectangles. Proc. 33rd FOCS (1992) 610–619.  Zbl0915.05039
  6. J. Kondev and Ch.L. Henley, Kac-Moody symmetries of critical ground states. Nuclear Phys. B464 (1996) 540–575.  Zbl1004.82501
  7. 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
  8. W. Magnus, A. Karass and D. Solitar, Combinatorial Group Theory. Dover Publications, Inc. (1976).  
  9. 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
  10. 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
  11. W.P. Thurston, Conway's tiling group. Amer. Math. Monthly (1990) 757–773.  Zbl0714.52007

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