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We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly…
Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the…
The aim of this paper is to propose a geometric framework for modelling similarity search in large and multidimensional data spaces of general nature, which seems to be flexible enough to address such issues as analysis of complexity,…
We consider the problem of computing a lightest derivation of a global structure using a set of weighted rules. A large variety of inference problems in AI can be formulated in this framework. We generalize A* search and heuristics derived…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…
In recent years, there has been renewed interest in closing the performance gap between state-of-the-art planning solvers and generalized planning (GP), a research area of AI that studies the automated synthesis of algorithmic-like…
Although heuristic search is one of the most successful approaches to classical planning, this planning paradigm does not apply straightforwardly to Generalized Planning (GP). This paper adapts the planning as heuristic search paradigm to…
Real-world point sets tend to be clustered, so using a machine word for each point is wasteful. In this paper we first show how a compact representation of quadtrees using $\Oh{1}$ bits per node can break this bound on clustered point sets,…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of…
In this paper, we describe the hyper-parameter search problem in the field of machine learning and present a heuristic approach in an attempt to tackle it. In most learning algorithms, a set of hyper-parameters must be determined before…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We face a need of discovering a pattern in locations of a great number of points in a high-dimensional space. Goal is to group the close points together. We are interested in a hierarchical structure, like a B-tree. B-Trees are…
We prove new parameterized complexity results for the FO Model Checking problem on a well-known generalization of interval and circular-arc graphs: the class of $H$-graphs, for any fixed multigraph $H$. In particular, we research how the…
The hypergraph-of-entity was conceptually proposed as a general model for entity-oriented search. However, only the performance for ad hoc document retrieval had been assessed. We continue this line of research by also evaluating ad hoc…
While systems designed for solving planning tasks vastly outperform Large Language Models (LLMs) in this domain, they usually discard the rich semantic information embedded within task descriptions. In contrast, LLMs possess parametrised…
Long-horizon planning in realistic environments requires the ability to reason over sequential tasks in high-dimensional state spaces with complex dynamics. Classical motion planning algorithms, such as rapidly-exploring random trees, are…
The classical Ham Sandwich theorem states that any $d$ point sets in $\mathbb{R}^d$ can be simultaneously bisected by a single affine hyperplane. A generalization of Dolnikov asserts that any $d$ families of pairwise intersecting compact,…