Ranked Enumeration for MSO on Trees via Knowledge Compilation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911761527996416 |
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| author | Amarilli, Antoine Bourhis, Pierre Capelli, Florent Monet, Mikaël |
| author_facet | Amarilli, Antoine Bourhis, Pierre Capelli, Florent Monet, Mikaël |
| contents | We study the problem of enumerating the satisfying assignments for circuit classes from knowledge compilation, where assignments are ranked in a specific order. In particular, we show how this problem can be used to efficiently perform ranked enumeration of the answers to MSO queries over trees, with the order being given by a ranking function satisfying a subset-monotonicity property.
Assuming that the number of variables is constant, we show that we can enumerate the satisfying assignments in ranked order for so-called multivalued circuits that are smooth, decomposable, and in negation normal form (smooth multivalued DNNF). There is no preprocessing and the enumeration delay is linear in the size of the circuit times the number of values, plus a logarithmic term in the number of assignments produced so far. If we further assume that the circuit is deterministic (smooth multivalued d-DNNF), we can achieve linear-time preprocessing in the circuit, and the delay only features the logarithmic term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_00731 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ranked Enumeration for MSO on Trees via Knowledge Compilation Amarilli, Antoine Bourhis, Pierre Capelli, Florent Monet, Mikaël Databases Data Structures and Algorithms Logic in Computer Science We study the problem of enumerating the satisfying assignments for circuit classes from knowledge compilation, where assignments are ranked in a specific order. In particular, we show how this problem can be used to efficiently perform ranked enumeration of the answers to MSO queries over trees, with the order being given by a ranking function satisfying a subset-monotonicity property. Assuming that the number of variables is constant, we show that we can enumerate the satisfying assignments in ranked order for so-called multivalued circuits that are smooth, decomposable, and in negation normal form (smooth multivalued DNNF). There is no preprocessing and the enumeration delay is linear in the size of the circuit times the number of values, plus a logarithmic term in the number of assignments produced so far. If we further assume that the circuit is deterministic (smooth multivalued d-DNNF), we can achieve linear-time preprocessing in the circuit, and the delay only features the logarithmic term. |
| title | Ranked Enumeration for MSO on Trees via Knowledge Compilation |
| topic | Databases Data Structures and Algorithms Logic in Computer Science |
| url | https://arxiv.org/abs/2310.00731 |