Ranked Enumeration for MSO on Trees via Knowledge Compilation

TL;DR

This paper introduces a method for efficiently enumerating MSO query answers over trees in ranked order using knowledge compilation techniques, with linear delay and preprocessing under certain circuit conditions.

Contribution

It presents a novel approach to ranked enumeration of MSO queries on trees using smooth multivalued DNNF circuits, with improved delay and preprocessing guarantees.

Findings

Enumeration delay is linear in circuit size and number of values plus a logarithmic term.

No preprocessing needed for smooth multivalued DNNF circuits.

Deterministic circuits allow linear-time preprocessing and reduced delay.

Abstract

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.