5 research outputs found
A Circuit-Based Approach to Efficient Enumeration
We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in knowledge compilation, a sub-area of artificial intelligence. We propose an algorithm for these circuits that enumerates valuations with linear preprocessing and delay linear in the Hamming weight of each valuation. Moreover, valuations of constant Hamming weight can be enumerated with linear preprocessing and constant delay.
Our results yield a framework for efficient enumeration that applies to all problems whose solutions can be compiled to structured d-DNNFs. In particular, we use it to recapture classical results in database theory, for factorized database representations and for MSO evaluation. This gives an independent proof of constant-delay enumeration for MSO formulae with first-order free variables on bounded-treewidth structures
Trade-offs in Static and Dynamic Evaluation of Hierarchical Queries
We investigate trade-offs in static and dynamic evaluation of hierarchical
queries with arbitrary free variables. In the static setting, the trade-off is
between the time to partially compute the query result and the delay needed to
enumerate its tuples. In the dynamic setting, we additionally consider the time
needed to update the query result in the presence of single-tuple inserts and
deletes to the input database.
Our approach observes the degree of values in the database and uses different
computation and maintenance strategies for high-degree and low-degree values.
For the latter it partially computes the result, while for the former it
computes enough information to allow for on-the-fly enumeration.
The main result of this work defines the preprocessing time, the update time,
and the enumeration delay as functions of the light/heavy threshold and of the
factorization width of the hierarchical query. By conveniently choosing this
threshold, our approach can recover a number of prior results when restricted
to hierarchical queries.
For a restricted class of hierarchical queries, our approach can achieve
worst-case optimal update time and enumeration delay conditioned on the Online
Matrix-Vector Multiplication Conjecture.Comment: Technical Report; 52 pages. The updated version contains: new
diagrams and plots summarizing known results and putting the results of the
paper into context; introduction of delta_i-hieararchical queries, for any
non-negative integer i; optimality results for delta_0- and
delta_1-hieararchical querie
Efficient enumeration for conjunctive queries over x-underbar structures
info:eu-repo/semantics/publishedComputer science logic (CSL