Wang tilings and distributed orientation on anonymous torus networks

Violet R. Syrotiuk; Charles J. Colbourn; Jan Pachl

doi:10.1007/3-540-57271-6_41

Wang tilings and distributed orientation on anonymous torus networks

Violet R. Syrotiuk, Charles J. Colbourn, Jan Pachl

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

This paper investigates the orientation problem on anonymous n×n torus networks. In the orientation problem, the goal is to reach an agreement, among all processors, on a consistent channel labelling. This paper shows that, if processors can label their channels arbitrarily, then there is no distributed orientation algorithm. Therefore the orientation problem is studied in various orientation models M that restrict local channel labellings. For many M, there are network labellings that, to the processors, are indistinguishable from orientations. These pseudo-orientations give rise to two problems related to orientation. In the verification problem, processors in an n×n torus distributively verify whether a network labelling in M is an orientation. The verification problem is shown to be equivalent to a problem of tiling the torus with Wang tiles. In the pseudo-orientation problem, the goal is to distributively find a pseudo-orientation. The pseudo-orientation problem is shown to be equivalent to a problem in graph theory.

Original language	English (US)
Title of host publication	Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings
Editors	Andre Schipe
Publisher	Springer Verlag
Pages	264-278
Number of pages	15
ISBN (Print)	9783540572718
DOIs	https://doi.org/10.1007/3-540-57271-6_41
State	Published - 1993
Externally published	Yes
Event	7th International Workshop on Distributed Algorithms, WDAG 1993 - Lausanne, Switzerland Duration: Sep 27 1993 → Sep 29 1993

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	725 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	7th International Workshop on Distributed Algorithms, WDAG 1993
Country/Territory	Switzerland
City	Lausanne
Period	9/27/93 → 9/29/93

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-57271-6_41

Cite this

Syrotiuk, V. R., Colbourn, C. J., & Pachl, J. (1993). Wang tilings and distributed orientation on anonymous torus networks. In A. Schipe (Ed.), Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings (pp. 264-278). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 725 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-57271-6_41

Wang tilings and distributed orientation on anonymous torus networks. / Syrotiuk, Violet R.; Colbourn, Charles J.; Pachl, Jan.

Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings. ed. / Andre Schipe. Springer Verlag, 1993. p. 264-278 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 725 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Syrotiuk, VR , Colbourn, CJ & Pachl, J 1993, Wang tilings and distributed orientation on anonymous torus networks. in A Schipe (ed.), Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 725 LNCS, Springer Verlag, pp. 264-278, 7th International Workshop on Distributed Algorithms, WDAG 1993, Lausanne, Switzerland, 9/27/93. https://doi.org/10.1007/3-540-57271-6_41

Syrotiuk VR , Colbourn CJ, Pachl J. Wang tilings and distributed orientation on anonymous torus networks. In Schipe A, editor, Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings. Springer Verlag. 1993. p. 264-278. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-57271-6_41

Syrotiuk, Violet R. ; Colbourn, Charles J. ; Pachl, Jan. / Wang tilings and distributed orientation on anonymous torus networks. Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings. editor / Andre Schipe. Springer Verlag, 1993. pp. 264-278 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{c126fe984b724f0cb0ac2dbf1a9847f3,

title = "Wang tilings and distributed orientation on anonymous torus networks",

abstract = "This paper investigates the orientation problem on anonymous n×n torus networks. In the orientation problem, the goal is to reach an agreement, among all processors, on a consistent channel labelling. This paper shows that, if processors can label their channels arbitrarily, then there is no distributed orientation algorithm. Therefore the orientation problem is studied in various orientation models M that restrict local channel labellings. For many M, there are network labellings that, to the processors, are indistinguishable from orientations. These pseudo-orientations give rise to two problems related to orientation. In the verification problem, processors in an n×n torus distributively verify whether a network labelling in M is an orientation. The verification problem is shown to be equivalent to a problem of tiling the torus with Wang tiles. In the pseudo-orientation problem, the goal is to distributively find a pseudo-orientation. The pseudo-orientation problem is shown to be equivalent to a problem in graph theory.",

author = "Syrotiuk, {Violet R.} and Colbourn, {Charles J.} and Jan Pachl",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1993.; 7th International Workshop on Distributed Algorithms, WDAG 1993 ; Conference date: 27-09-1993 Through 29-09-1993",

year = "1993",

doi = "10.1007/3-540-57271-6_41",

language = "English (US)",

isbn = "9783540572718",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "264--278",

editor = "Andre Schipe",

booktitle = "Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings",

}

TY - GEN

T1 - Wang tilings and distributed orientation on anonymous torus networks

AU - Syrotiuk, Violet R.

AU - Colbourn, Charles J.

AU - Pachl, Jan

PY - 1993

Y1 - 1993

N2 - This paper investigates the orientation problem on anonymous n×n torus networks. In the orientation problem, the goal is to reach an agreement, among all processors, on a consistent channel labelling. This paper shows that, if processors can label their channels arbitrarily, then there is no distributed orientation algorithm. Therefore the orientation problem is studied in various orientation models M that restrict local channel labellings. For many M, there are network labellings that, to the processors, are indistinguishable from orientations. These pseudo-orientations give rise to two problems related to orientation. In the verification problem, processors in an n×n torus distributively verify whether a network labelling in M is an orientation. The verification problem is shown to be equivalent to a problem of tiling the torus with Wang tiles. In the pseudo-orientation problem, the goal is to distributively find a pseudo-orientation. The pseudo-orientation problem is shown to be equivalent to a problem in graph theory.

AB - This paper investigates the orientation problem on anonymous n×n torus networks. In the orientation problem, the goal is to reach an agreement, among all processors, on a consistent channel labelling. This paper shows that, if processors can label their channels arbitrarily, then there is no distributed orientation algorithm. Therefore the orientation problem is studied in various orientation models M that restrict local channel labellings. For many M, there are network labellings that, to the processors, are indistinguishable from orientations. These pseudo-orientations give rise to two problems related to orientation. In the verification problem, processors in an n×n torus distributively verify whether a network labelling in M is an orientation. The verification problem is shown to be equivalent to a problem of tiling the torus with Wang tiles. In the pseudo-orientation problem, the goal is to distributively find a pseudo-orientation. The pseudo-orientation problem is shown to be equivalent to a problem in graph theory.

UR - http://www.scopus.com/inward/record.url?scp=84885691346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885691346&partnerID=8YFLogxK

U2 - 10.1007/3-540-57271-6_41

DO - 10.1007/3-540-57271-6_41

M3 - Conference contribution

AN - SCOPUS:84885691346

SN - 9783540572718

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 264

EP - 278

BT - Distributed Algorithms - 7th International Workshop, WDAG 1993, Proceedings

A2 - Schipe, Andre

PB - Springer Verlag

T2 - 7th International Workshop on Distributed Algorithms, WDAG 1993

Y2 - 27 September 1993 through 29 September 1993

ER -

Wang tilings and distributed orientation on anonymous torus networks

Abstract

Publication series

Other

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this