TY - GEN

T1 - Wang tilings and distributed orientation on anonymous torus networks

AU - Syrotiuk, Violet R.

AU - Colbourn, Charles J.

AU - Pachl, Jan

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1993.

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.

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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 -