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The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
Planning under uncertainty is critical for robust robot performance in uncertain, dynamic environments, but it incurs high computational cost. State-of-the-art online search algorithms, such as DESPOT, have vastly improved the computational…
Recent advancements in generative large language models (LLMs) have significantly boosted the performance in natural language processing tasks. However, their efficiency is hampered by the inherent limitations in autoregressive token…
Hyperdimensional Computing (HDC) is emerging as a promising approach for edge AI, offering a balance between accuracy and efficiency. However, current HDC-based applications often rely on high-precision models and/or encoding matrices to…
In generating large quantities of DNA data, high-throughput sequencing technologies require advanced bioinformatics infrastructures for efficient data analysis. k-mer counting, the process of quantifying the frequency of fixed-length k DNA…
Recent advancements have significantly enhanced the performance of large language models (LLMs) in tackling complex reasoning tasks, achieving notable success in domains like mathematical and logical reasoning. However, these methods…
Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes…
Discovering dense subgraphs and understanding the relations among them is a fundamental problem in graph mining. We want to not only identify dense subgraphs, but also build a hierarchy among them (e.g., larger but sparser subgraphs formed…
This paper presents new parallel algorithms for generating Euclidean minimum spanning trees and spatial clustering hierarchies (known as HDBSCAN$^*$). Our approach is based on generating a well-separated pair decomposition followed by using…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
An optimal data partitioning in parallel & distributed implementation of clustering algorithms is a necessary computation as it ensures independent task completion, fair distribution, less number of affected points and better & faster…
Counting the number of answers to conjunctive queries is a fundamental problem in databases that, under standard assumptions, does not have an efficient solution. The issue is inherently #P-hard, extending even to classes of acyclic…
Combinatorial branch and bound searches are a common technique for solving global optimisation and decision problems. Their performance often depends on good search order heuristics, refined over decades of algorithms research. Parallel…
We present a deterministic parallel multilevel algorithm for balanced hypergraph partitioning that matches the state of the art for non-deterministic algorithms. Deterministic parallel algorithms produce the same result in each invocation,…
We formally introduce a systematic (de/re)-composition approach, based on the algebraic formalism of "Multi-Dimensional Homomorphisms (MDHs)". Our approach is designed as general enough to be applicable to a wide range of data-parallel…
The High Luminosity upgrade of the Large Hadron Collider (HL-LHC) will produce particle collisions with up to 200 simultaneous proton-proton interactions. These unprecedented conditions will create a combinatorial complexity for…
The $k^2$-tree is a compact data structure designed to efficiently store sparse binary matrices by leveraging both sparsity and clustering of nonzero elements. This representation supports efficiently navigational operations and complex…
Finding the dense regions of a graph and relations among them is a fundamental problem in network analysis. Core and truss decompositions reveal dense subgraphs with hierarchical relations. The incremental nature of algorithms for computing…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…