Compression with wildcards: All induced metric subgraphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910721649934336 |
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| author | Wild, Marcel |
| author_facet | Wild, Marcel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compression with wildcards: All induced metric subgraphs Wild, Marcel Combinatorics Data Structures and Algorithms 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. |
| title | Compression with wildcards: All induced metric subgraphs |
| topic | Combinatorics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2409.08363 |