Related papers: mqr-tree: A 2-dimensional Spatial Access Method
High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional…
The representation of binary relations has been intensively studied and many different theoretical and practical representations have been proposed to answer the usual queries in multiple domains. However, ternary relations have not…
We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…
Motion planning is challenging when it comes to the case of imperfect state information. Decision should be made based on belief state which evolves according to the noise from the system dynamics and sensor measurement. In this paper, we…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
In this paper two new graph operations are introduced, and with them the S-trees are studied in depth. This allows to find \(\{-1,0,1\}\)-basis for all the fundamental subspaces of the adjacency matrix of any tree, and to understand in…
LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…
This paper proposed a new methodology for machine learning in 2-dimensional space (2-D ML) in inline coordinates. It is a full machine learning approach that does not require to deal with n-dimensional data in n-dimensional space. It allows…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…
This paper presents a Riemannian metric-based model to solve the optimal path planning problem on two-dimensional smooth submanifolds in high-dimensional space. Our model is based on constructing a new Riemannian metric on a two-dimensional…
Multi-modal data is becoming more common in big data background. Finding the semantically similar objects from different modality is one of the heart problems of multi-modal learning. Most of the current methods try to learn the inter-modal…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
Multi-robot autonomous exploration in an unknown environment is an important application in robotics.Traditional exploration methods only use information around frontier points or viewpoints, ignoring spatial information of unknown areas.…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
The Maximum Common Subgraph (MCS) problem plays a key role in many applications, including cheminformatics, bioinformatics, and pattern recognition, where it is used to identify the largest shared substructure between two graphs. Although…
Achieving bound consistency for the no-overlap constraint is known to be NP-complete. Therefore, several polynomial-time tightening techniques, such as edge finding, not-first-not-last reasoning, and energetic reasoning, have been…
In order to make full use of geographic routing techniques developed for sensor networks, nodes must be localized. However, traditional localization and virtual localization techniques are dependent either on expensive and sometimes…
Motion Planning is necessary for robots to complete different tasks. Rapidly-exploring Random Tree (RRT) and its variants have been widely used in robot motion planning due to their fast search in state space. However, they perform not well…