Oracles for vertex elimination orderings

AbstractBy maintaining appropriate data structures, we develop constant-time transposition oracles that answer whether or not two adjacent vertices in a simple elimination ordering (SEO) or a semiperfect elimination ordering (semiPEO) can be swapped to produce a new SEO or semiPEO, respectively. Combined with previous results regarding convex geometries and antimatroids, this allows us to list all SEOs of a strongly chordal graph and all semiPEOs of an HHDA-free graph in Gray code order. By applying a new amortized analysis we show that the algorithms run in constant amortized time.Additionally, we provide a simple framework that can be used to exhaustively list the basic words for other antimatroids