A sequence d of integers is a degree sequence if there exists a (simple) graph G such that the components of d are equal to the degrees of the vertices of G. The graph G is said to be a realization of d. We provide an efficient parallel algorithm to realize d; the algorithm runs in O(log n) me using O(n + m) CRCW PRAM processors, where n and m are the number of vertices and edges G. Before our result, it was not known if the problem of realizing d is in NC.

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Keywords Degree quence, Design and analysis of algorithms, Graph algorithms, Majorization, Parallel computation, PRAM
Persistent URL dx.doi.org/10.1137/S0895480194267932
Journal SIAM Journal on Discrete Mathematics
Arikati, S.R. (Srinivasa R.), & Maheshwari, A. (1996). Realizing degree sequences in parallel. SIAM Journal on Discrete Mathematics, 9(2), 317–338. doi:10.1137/S0895480194267932