2024/09/12 by Marcel Wild, Wild, Marcel
Computer Science · #Advanced Image and Video Retrieval Techniques #Algorithms and Data Compression #Combinatorics (math.CO) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2409.08363
openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Driven by applications in the natural, social and computer sciences several algorithms have been proposed to enumerate all sets X\s V of vertices of a graph G=(V,E) that induce a \it connected subgraph. We offer two algorithms for enumerating all X's that induce (more exquisite) \it metric subgraphs. Specifically, the first algorithm, called \tt AllMetricSets, generates these X's in a compressed format. The second algorithm generates all (accessible) metric sets one-by-one but is provably output-polynomial. Mutatis mutandis the same holds for the geodesically-convex sets X\s V, this being a natural strengthening of "metric". The Mathematica command \tt BooleanConvert features prominently.