no. 3
Algebraic tools for the construction of colored flows with boundary constraints
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 3, pp. 229-243.

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.

DOI : 10.1051/ita:2004011
Classification : 05C25, 05C85
Mots clés : height function, planar flows 
@article{ITA_2004__38_3_229_0,
     author = {Dorkenoo, Marius and Eglin-Leclerc, Marie-Christine and R\'emila, Eric},
     title = {Algebraic tools for the construction of colored flows with boundary constraints},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {229--243},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {3},
     year = {2004},
     doi = {10.1051/ita:2004011},
     mrnumber = {2076401},
     zbl = {1060.05055},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2004011/}
}
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 - Informatique Théorique et Applications
PY  - 2004
SP  - 229
EP  - 243
VL  - 38
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2004011/
DO  - 10.1051/ita:2004011
LA  - en
ID  - ITA_2004__38_3_229_0
ER  - 
%0 Journal Article
%A Dorkenoo, Marius
%A Eglin-Leclerc, Marie-Christine
%A Rémila, Eric
%T Algebraic tools for the construction of colored flows with boundary constraints
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2004
%P 229-243
%V 38
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ita:2004011/
%R 10.1051/ita:2004011
%G en
%F ITA_2004__38_3_229_0
Dorkenoo, Marius; Eglin-Leclerc, Marie-Christine; Rémila, Eric. Algebraic tools for the construction of colored flows with boundary constraints. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 3, pp. 229-243. doi : 10.1051/ita:2004011. http://www.numdam.org/articles/10.1051/ita:2004011/

[1] T. Chaboud, Pavages et Graphes de Cayley. Ph.D. Thesis, École Normale Supérieure de Lyon (1995).

[2] J.H. Conway and J.C. Lagarias, Tiling with Polyominoes and Combinatorial Group Theory. J. Combin. Theory A 53 (1990) 183-208. | Zbl

[3] R. Hassin, Maximum flows in (s,t) planar networks. Inform. Proc. Lett. 13 (1981) 107. | MR

[4] R. Hassin and D.B. Johnson, An O(nlog 2 n) algorithm for maximum flow in undirected planar networks. SIAM J. Comput. 14 (1985) 612-624. | Zbl

[5] C. Kenyon and R. Kenyon, Tiling a polygon with rectangles. Proc. 33rd FOCS (1992) 610-619. | Zbl

[6] J. Kondev and Ch.L. Henley, Kac-Moody symmetries of critical ground states. Nuclear Phys. B 464 (1996) 540-575. | Zbl

[7] J.C. Lagarias and D.S. Romano, A Polyomino Tiling of Thurston and its Configurational Entropy. J. Combin. Theory A 63 (1993) 338-358. | Zbl

[8] W. Magnus, A. Karass and D. Solitar, Combinatorial Group Theory. Dover Publications, Inc. (1976). | MR | Zbl

[9] J. Propp, A pedestrian approach to a method of Conway, or a tale of two cities. Internal Report, Massachusetts Institute of Technology (1993). | Zbl

[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. | Zbl

[11] W.P. Thurston, Conway's tiling group. Amer. Math. Monthly (1990) 757-773. | Zbl

Cité par Sources :