Related papers: Generalized comparison trees for point-location pr…
This paper presents new methods for analyzing and evaluating generalized plans that can solve broad classes of related planning problems. Although synthesis and learning of generalized plans has been a longstanding goal in AI, it remains…
In retrieval-augmented systems, context ranking techniques are commonly employed to reorder the retrieved contexts based on their relevance to a user query. A standard approach is to measure this relevance through the similarity between…
The problem of relocating a set of objects to designated areas amidst movable obstacles can be framed as a Geometric Task and Motion Planning (G-TAMP) problem, a subclass of task and motion planning (TAMP). Traditional approaches to G-TAMP…
Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…
This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
A \emph{general branch-and-bound tree} is a branch-and-bound tree which is allowed to use general disjunctions of the form $\pi^{\top} x \leq \pi_0 \,\vee\, \pi^{\top}x \geq \pi_0 + 1$, where $\pi$ is an integer vector and $\pi_0$ is an…
Within a mathematically rigorous model, we analyse the curse of dimensionality for deterministic exact similarity search in the context of popular indexing schemes: metric trees. The datasets $X$ are sampled randomly from a domain $\Omega$,…
Pattern tree are based on integrated rules which are equal to a combination of some points connected to each other in a hierarchical structure, called Enquiry Hierarchical (EH). The main operation in pattern enquiry seeking is to locate the…
This paper introduces a novel tree-based model, Learning Hyperplane Tree (LHT), which outperforms state-of-the-art (SOTA) tree models for classification tasks on several public datasets. The structure of LHT is simple and efficient: it…
Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…
We study planar point location in a collection of disjoint fat regions, and investigate the complexity of \emph {local updates}: replacing any region by a different region that is "similar" to the original region. (i.e., the size differs by…
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as…
Accurate and efficient entity resolution (ER) is a significant challenge in many data mining and analysis projects requiring integrating and processing massive data collections. It is becoming increasingly important in real-world…
For a reduced hyperplane arrangement we prove the analytic Twisted Logarithmic Comparison Theorem, subject to mild combinatorial arithmetic conditions on the weights defining the twist. This gives a quasi-isomorphism between the twisted…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
We propose a family of search directions based on primal-dual entropy in the context of interior-point methods for linear optimization. We show that by using entropy based search directions in the predictor step of a predictor-corrector…
As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery…
We present a simple geometric framework for the relational join. Using this framework, we design an algorithm that achieves the fractional hypertree-width bound, which generalizes classical and recent worst-case algorithmic results on…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…