Parallel O(log n) time edge-colouring of trees and Halin graphs

Abstract

We present parallel O(log(n))-time algorithms for optimal edge colouring of trees and Halin graphs with n processors on a a parallel random access machine without write conflicts (P-RAM). In the case of Halin graphs with a maximum degree of three, the colouring algorithm automatically finds every Hamiltonian cycle of the graph. PARALLEL O(LOG(N)) TIME EDGE-COLOURING OF TREES AND HALIN GRAPHSAlan Gibbons(1), Amos Israeli(2) and Wojciech Rytter(13) AbstractWe present parallel O(log(n))-time algorithms for optimal edge colouring of trees and Halin graphs with n processors on a parallel random access machine without write conflicts (P-RAM). In the case of Halin graphs with a maximum degree of three, the colouring algorithm automatically finds every Hamiltonian cycle of the graph.

Euler Meets GPU: Practical Graph Algorithms with Theoretical Guarantees

“…Later the technique was used in many PRAM algorithms from different areas, e.g. algorithms on trees [14,23], planar graphs [22,44], polygons [24], texts [12,16], and context-free grammars [47]. It also found applications beyond PRAM, e.g.…”

Optimally edge-colouring outerplanar graphs is in NC

“…In [7] it was implied that the problems of optimally edge-colouring outerplanar and Halin graphs are both in NC. In co-authorship with Amos Israeli and since presenting [7], the present authors discovered an improved algorithm for Hein graphs which is described in [6].…”