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Modern applied optimization problems become more and more complex every day. Due to this fact, distributed algorithms that can speed up the process of solving an optimization problem through parallelization are of great importance. The main…
This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems,…
We introduce a new spatial data structure for high dimensional data called the \emph{approximate principal direction tree} (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy…
The original description of the k-d tree recognized that rebalancing techniques, such as are used to build an AVL tree or a red-black tree, are not applicable to a k-d tree. Hence, in order to build a balanced k-d tree, it is necessary to…
We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…
Transformers are widely used deep learning architectures. Existing transformers are mostly designed for sequences (texts or time series), images or videos, and graphs. This paper proposes a novel transformer model for massive (up to a…
Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…
We present an approach for efficiently taking snapshots of the state of a collection of CAS objects. Taking a snapshot allows later operations to read the value that each CAS object had at the time the snapshot was taken. Taking a snapshot…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…
Transformers have been successful in many vision tasks, thanks to their capability of capturing long-range dependency. However, their quadratic computational complexity poses a major obstacle for applying them to vision tasks requiring…
Distributed optimization algorithms have emerged as a superior approaches for solving machine learning problems. To accommodate the diverse ways in which data can be stored across devices, these methods must be adaptable to a wide range of…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers specific queries pertinent to the problem at hand. In this work, we address the fully dynamic edge orientation problem, also…
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…
A set of n points in low dimensions takes Theta(n w) bits to store on a w-bit machine. Surface reconstruction and mesh refinement impose a requirement on the distribution of the points they process. I show how to use this assumption to…
Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a…
Motivation: As a fundamental task in bioinformatics, searching for massive short patterns over a long text is widely accelerated by various compressed full-text indexes. These indexes are able to provide similar searching functionalities to…
Algebraic data structures are the main subroutine for maintaining distances in fully dynamic graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot maintain the shortest paths, especially against adaptive…
A fully threaded tree (FTT) for adaptive refinement of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications are…
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…