Affiliation:
1. Université Paris 7, Paris cedex, France
2. Université de Caen, Caen cedex, France
Abstract
A relational structure is
d
-degree-bounded, for some integer
d
, if each element of the domain belongs to at most
d
tuples. In this paper, we revisit the complexity of the evaluation problem of not necessarily Boolean first-order (
FO
) queries over
d
-degree-bounded structures. Query evaluation is considered here as a dynamical process. We prove that any
FO
query on
d
-degree-bounded structures belongs to the complexity class constant-Delay
lin
, that is, can be computed by an algorithm that has two separate parts: it has a precomputation step of time linear in the size of the structure and then, it outputs all solutions (i.e., tuples that satisfy the formula) one by one with a constant delay (i.e., depending on the size of the formula only) between each. Seen as a global process, this implies that queries on
d
-degree-bounded structures can be evaluated in total time
f
(|φ|).(|
S
| + |φ(
S
)|) and space
g
(|φ|).|
S
| where
S
is the structure, φ is the formula, φ(
S
) is the result of the query and
f
,
g
are some fixed functions.
Among other things, our results generalize a result of Seese on the data complexity of the model-checking problem for
d
-degree-bounded structures. Besides, the originality of our approach compared to related results is that it does not rely on the Hanf's model-theoretic technique and is simple and informative since it essentially rests on a quantifier elimination method.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Cited by
45 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Recent Increments in Incremental View Maintenance;Companion of the 43rd Symposium on Principles of Database Systems;2024-06-09
2. F-IVM: analytics over relational databases under updates;The VLDB Journal;2023-11-14
3. Trade-offs in Static and Dynamic Evaluation of Hierarchical Queries;Logical Methods in Computer Science;2023-08-09
4. Faster Property Testers in a Variation of the Bounded Degree Model;ACM Transactions on Computational Logic;2023-05-10
5. Efficient Enumeration for Annotated Grammars;Proceedings of the 41st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems;2022-06-12