ENUMERATING ALL CYCLES OF A PLANAR GRAPH - DOG¯RUSÖZ, U.; KRISHNAMOORTHY, M. S. (Parallel algorithms and applications, 1996)
We present a new and elegant cycle vector space algorithm that runs in O(n 2 .α) steps and needs O:lpar;nn) space for enumerating all simple cycles of a planar graph with n vertices, where α is the total number of simple cycles in the graph Unlike backtrack algorithms, cycle vector space algorithms for this problem are suitable for parallelization. A parallel version of this algorithm alone with a parallel version of Syslo's O(n.α) step algorithm for the same problem are on an exclusive-read, exclusive-write parallel RAM model with p processors. The results of an implementation of our parallel algorithm on a meshconnected SIMD computer are also presented.