Related papers: Query maintenance under batch changes with small-d…
A database D may be inconsistent wrt a given set IC of integrity constraints. Consistent Query Answering (CQA) is the problem of computing from D the answers to a query that are consistent wrt IC . Consistent answers are invariant under all…
We study the complexity of consistent query answering on databases that may violate primary key constraints. A repair of such a database is any consistent database that can be obtained by deleting a minimal set of tuples. For every Boolean…
Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main…
In the dynamic tree problem the goal is the maintenance of an arbitrary n-vertex forest, where the trees are subject to joining and splitting by, respectively, adding and removing edges. Depending on the application, information can be…
We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…
A class of relational databases has low degree if for all $\delta>0$, all but finitely many databases in the class have degree at most $n^{\delta}$, where $n$ is the size of the database. Typical examples are databases of bounded degree or…
The performance of a dynamic dictionary is measured mainly by its update time, lookup time, and space consumption. In terms of update time and lookup time there are known constructions that guarantee constant-time operations in the worst…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
We study the data complexity of consistent query answering (CQA) on databases that may violate the primary key constraints. A repair is a maximal consistent subset of the database. For a Boolean query $q$, the problem…
We consider the dynamic dictionary problem for multisets. Given an upper bound $n$ on the total cardinality of the multiset (i.e., including multiplicities) at any point in time, the goal is to design a data structure that supports…
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering…
We say an algorithm is batch size-invariant if changes to the batch size can largely be compensated for by changes to other hyperparameters. Stochastic gradient descent is well-known to have this property at small batch sizes, via the…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to…
The framework of consistent query answers and repairs has been introduced to alleviate the impact of inconsistent data on the answers to a query. A repair is a minimally different consistent instance and an answer is consistent if it is…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
We investigate the complexity of uniform OR circuits and AND circuits of polynomial-size and depth. As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant (0/1) gates.…
Explaining why a language model produces a particular output requires local, input-level explanations. Existing methods uncover global capability circuits (e.g., indirect object identification), but not why the model answers a specific…
Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range query and update operations. A Segment Tree divides the…
Despite exceptional capabilities in knowledge-intensive tasks, Large Language Models (LLMs) face a critical gap in understanding how they internalize new knowledge, particularly how to structurally embed acquired knowledge in their neural…