Dynamic Complexity under Definable Changes
Dynamic Complexity under Definable Changes
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可定义变化下的动态复杂性
DOI：
10.1145/3241040
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
T. Zeume
中科院分区：
文献类型：
--
作者：
T. Schwentick;N. Vortmeier;T. Zeume
在动态复杂性的设置中，动态程序的目的是维护固定查询的结果，该查询会使用更改，换句话说，换句话说，动态程序会更新一个实质性的视图。基本关系已更改。
Patnaik和Immerman的原始框架仅考虑插入或删除单个元组的数据库。更具体地，操作表明，无向接收查询是在单匹培训变化和一阶定义插入下保持一阶的免费的一阶查询。
这些结果依赖于有界的桥梁属性，基本上说，在插入定义的边缘之后，对于每个连接的节点，都有一些有界数的新边缘的路径。 ，它显示出由联合查询工会定义的插入查询，以说明这种限制设置的结果实际上是相关的，它们通过一项实验研究完成，将动态程序的性能与复杂变化，动态性，动态性，动态性更改进行了比较具有单个更改的程序，并从头开始进行评论。
积极的结果由几个不可表达的结果完成。
最后，提出了与反应无关的进一步的积极结果：这表明，对于由无参数的一阶公式定义的变化，所有logspace定义（甚至AC1定义）的查询都可以通过一阶动力程序来维持。
In the setting of dynamic complexity, the goal of a dynamic program is to maintain the result of a fixed query for an input database that is subject to changes, possibly using additional auxiliary relations. In other words, a dynamic program updates a materialized view whenever a base relation is changed. The update of query result and auxiliary relations is specified using first-order logic or, equivalently, relational algebra.
The original framework by Patnaik and Immerman only considers changes to the database that insert or delete single tuples. This article extends the setting to definable changes, also specified by first-order queries on the database, and generalizes previous maintenance results to these more expressive change operations. More specifically, it is shown that the undirected reachability query is first-order maintainable under single-tuple changes and first-order defined insertions, likewise the directed reachability query for directed acyclic graphs is first-order maintainable under insertions defined by quantifier-free first-order queries.
These results rely on bounded bridge properties, which basically say that, after an insertion of a defined set of edges, for each connected pair of nodes there is some path with a bounded number of new edges. While this bound can be huge, in general, it is shown to be small for insertion queries defined by unions of conjunctive queries. To illustrate that the results for this restricted setting could be practically relevant, they are complemented by an experimental study that compares the performance of dynamic programs with complex changes, dynamic programs with single changes, and with recomputation from scratch.
The positive results are complemented by several inexpressibility results. For example, it is shown that—unlike for single-tuple insertions—dynamic programs that maintain the reachability query under definable, quantifier-free changes strictly need update formulas with quantifiers.
Finally, further positive results unrelated to reachability are presented: it is shown that for changes definable by parameter-free first-order formulas, all LOGSPACE-definable (and even AC1-definable) queries can be maintained by first-order dynamic programs.
多次变化下的可达性和距离
DOI：
10.4230/lipics.icalp.2018.120
发表时间：
2018
期刊：
影响因子：
--
作者：
Samir Datta;Anish Mukherjee;Nils Vortmeier;Thomas Zeume
通讯作者：
Thomas Zeume
k-clique的动态描述复杂度
DOI：
10.1016/j.ic.2017.04.005
发表时间：
2017
期刊：
Inf. Comput.
影响因子：
--
作者：
Thomas Zeume
通讯作者：
Thomas Zeume
动态连接查询
DOI：
10.1016/j.jcss.2017.03.014
发表时间：
2017
期刊：
影响因子：
--
作者：
Thomas Zeume;Thomas Schwentick
通讯作者：
Thomas Schwentick