Publications [#337716] of John H. Reif

Conference articles PUBLISHED

1. Filotti, IS; Miller, GL; Reif, J, On determining the genus of a graph in 0(V0(g)) steps, Proceedings of the Annual ACM Symposium on Theory of Computing (April, 1979), pp. 27-37, ACM Press [pdf], [doi]
   (last updated on 2026/01/14)

   Abstract:
   Putting all the procedures together we can obtain our genus algorithm. Procedure. Embedding (G,g) (1) Generate Basic Subgraph (G,g), say Lj. (2) Remove Internal Edges (G,L,I). (3) Partition (G,L,I). (4) Quasiplanar (G,L,I). (5) 2-CNF (G,L,I). We can now analyze the running time of Embedding. We list the multiplicative factors for each of the steps (1) to (4): (1) 0((eg).e2g) (2) and (3) 0(e188g) (4) 0((56g)336g). Note that each of these terms is bounded by (g-v)0^. We state this as a theorem: Theorem 1. There exists an algorithm to determine the genus of graph which runs in (g-v)0(g) time. By running Embedding on inputs for successively larger g we can determine the genus of a graph.