This paper considers an integrated sensing and communication system where a multi-antenna base station transmits a common signal for joint multi-user communication and extend target (ET) sensing. We first propose a second-order truncated Fourier series surface model for an arbitrarily-shaped three-dimensional (3D) ET, characterized by center range, center elevation, center azimuth, orientation, and surface coefficients. Based on this model, we consider the backscattering effects of the visible elements along the ET surface, and derive novel closed-form Cramér-Rao bounds (CRBs) for the ET characteristic parameter estimation. Further, we formulate a CRB minimization problem by optimizing the transmit beamformers, under the constraints of transmit power budget, communication-specific signal-to-interference-plus-noise requirements, and ET-specific beam coverage requirement. The non-convex optimization problem can be efficiently solved by the semidefinite relaxation technique. Numerical results demonstrate that the proposed beamforming design is superior to existing baselines with significantly lower CRBs and a more appropriate beampattern for sensing a 3D ET.

This paper studies an integrated sensing and communication (ISAC) system, where a multi-antenna base station transmits beamformed signals for joint downlink multi-user communication and radar sensing of an extended target (ET). By considering echo signals as reflections from valid elements on the ET contour, a set of novel Cramér-Rao bounds (CRBs) is derived for parameter estimation of the ET, including central range, direction, and orientation. The ISAC transmit beamforming design is then formulated as an optimization problem, aiming to minimize the CRB associated with radar sensing, while satisfying a minimum signal-to-interference-pulse-noise ratio requirement for each communication user, along with a 3-dB beam coverage constraint tailored for the ET. To solve this non-convex problem, we utilize semidefinite relaxation (SDR) and propose a rank-one solution extraction scheme for non-tight relaxation circumstances. To reduce the computation complexity, we further employ an efficient zero-forcing (ZF) based beamforming design, where the sensing task is performed in the null space of communication channels. Numerical results validate the effectiveness of the obtained CRB, revealing the diverse features of CRB for differently shaped ETs. The proposed SDR beamforming design outperforms benchmark designs with lower estimation error and CRB, while the ZF beamforming design greatly improves computation efficiency with minor sensing performance loss.

This paper presents ParGeo, a multicore library for computational geometry. ParGeo contains modules for fundamental tasks including $k$d-tree based spatial search, spatial graph generation, and algorithms in computational geometry. We focus on three new algorithmic contributions provided in the library. First, we present a new parallel convex hull algorithm based on a reservation technique to enable parallel modifications to the hull. We also provide the first parallel implementations of the randomized incremental convex hull algorithm as well as a divide-and-conquer convex hull algorithm in $\mathbb{R}^3$. Second, for the smallest enclosing ball problem, we propose a new sampling-based algorithm to quickly reduce the size of the data set. We also provide the first parallel implementation of Welzl's classic algorithm for smallest enclosing ball. Third, we present the BDL-tree, a parallel batch-dynamic $k$d-tree that allows for efficient parallel updates and $k$-NN queries over dynamically changing point sets. BDL-trees consist of a log-structured set of $k$d-trees which can be used to efficiently insert, delete, and query batches of points in parallel. On 36 cores with two-way hyper-threading, our fastest convex hull algorithm achieves up to 44.7x self-relative parallel speedup and up to 559x speedup against the best existing sequential implementation. Our smallest enclosing ball algorithm using our sampling-based algorithm achieves up to 27.1x self-relative parallel speedup and up to 178x speedup against the best existing sequential implementation. Our implementation of the BDL-tree achieves self-relative parallel speedup of up to 46.1x. Across all of the algorithms in ParGeo, we achieve self-relative parallel speedup of 8.1--46.61x.

We present ParGeo, a multicore library for computational geometry algorithms. We describe two of the algorithms from ParGeo, convex hull and the smallest enclosing ball, and present a short evaluation of all implementations currently in ParGeo.

We propose a theoretically-efficient and practical parallel batch-dynamic data structure for the closest pair problem. Our solution is based on a serial dynamic closest pair data structure by Golin et al., and supports batches of insertions and deletions in parallel. For a data set of size $n$, our data structure supports a batch of insertions or deletions of size $m$ in $O(m(1+\log ((n+m)/m)))$ expected work and $O(\log (n+m)\log^*(n+m))$ depth with high probability, and takes linear space. The key techniques for achieving these bounds are a new work-efficient parallel batch-dynamic binary heap, and careful management of the computation across sets of points to minimize work and depth. We provide an optimized multicore implementation of our data structure using dynamic hash tables, parallel heaps, and dynamic $k$-d trees. Our experiments on a variety of synthetic and real-world data sets show that it achieves a parallel speedup of up to 38.57x (15.10x on average) on 48 cores with hyper-threading. In addition, we also implement and compare four parallel algorithms for static closest pair problem, for which we are not aware of any existing practical implementations. On 48 cores with hyper-threading, the static algorithms achieve up to 51.45x (29.42x on average) speedup, and Rabin's algorithm performs the best on average. Comparing our dynamic algorithm to the fastest static algorithm, we find that it is advantageous to use the dynamic algorithm for batch sizes of up to 20\% of the data set. As far as we know, our work is the first to experimentally evaluate parallel closest pair algorithms, in both the static and the dynamic settings.

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 Kruskal's minimum spanning tree algorithm and bichromatic closest pair computations. We introduce a new notion of well-separation to reduce the work and space of our algorithm for HDBSCAN*. We also give a new parallel divide-and-conquer algorithm for computing the dendrogram and reachability plots, which are used in visualizing clusters of different scale that arise for both EMST and HDBSCAN*. We show that our algorithms are theoretically efficient: they have work (number of operations) matching their sequential counterparts, and polylogarithmic depth (parallel time).

This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative clustering (HAC) algorithms, and using the framework we obtain novel parallel algorithms for the complete linkage, average linkage, and Ward's linkage criteria. Compared to most previous parallel HAC algorithms, which require quadratic memory, our new algorithms require only linear memory, and are scalable to large data sets. ParChain is based on our parallelization of the nearest-neighbor chain algorithm, and enables multiple clusters to be merged on every round. We introduce two key optimizations that are critical for efficiency: a range query optimization that reduces the number of distance computations required when finding nearest neighbors of clusters, and a caching optimization that stores a subset of previously computed distances, which are likely to be reused. Experimentally, we show that our highly-optimized implementations using 48 cores with two-way hyper-threading achieve 5.8--110.1x speedup over state-of-the-art parallel HAC algorithms and achieve 13.75--54.23x self-relative speedup. Compared to state-of-the-art algorithms, our algorithms require up to 237.3x less space. Our algorithms are able to scale to data set sizes with tens of millions of points, which existing algorithms are not able to handle.

The DBSCAN method for spatial clustering has received significant attention due to its applicability in a variety of data analysis tasks. There are fast sequential algorithms for DBSCAN in Euclidean space that take O(nłog n) work for two dimensions, sub-quadratic work for three or more dimensions, and can be computed approximately in linear work for any constant number of dimensions. However, existing parallel DBSCAN algorithms require quadratic work in the worst case. This paper bridges the gap between theory and practice of parallel DBSCAN by presenting new parallel algorithms for Euclidean exact DBSCAN and approximate DBSCAN that match the work bounds of their sequential counterparts, and are highly parallel (polylogarithmic depth). We present implementations of our algorithms along with optimizations that improve their practical performance. We perform a comprehensive experimental evaluation of our algorithms on a variety of datasets and parameter settings. Our experiments on a 36-core machine with two-way hyper-threading show that our implementations outperform existing parallel implementations by up to several orders of magnitude, and achieve speedups of up to 33x over the best sequential algorithms.

In the last decade, it has been shown that many hard AI tasks, especially in NLP, can be naturally modeled as extreme classification problems leading to improved precision. However, such models are prohibitively expensive to train due to the memory bottleneck in the last layer. For example, a reasonable softmax layer for the dataset of interest in this paper can easily reach well beyond 100 billion parameters (> 400 GB memory). To alleviate this problem, we present Merged-Average Classifiers via Hashing (MACH), a generic $K$-classification algorithm where memory provably scales at $O(\log K)$ without any assumption on the relation between classes. MACH is subtly a count-min sketch structure in disguise, which uses universal hashing to reduce classification with a large number of classes to few embarrassingly parallel and independent classification tasks with a small (constant) number of classes. MACH naturally provides a technique for zero communication model parallelism. We experiment with 6 datasets; some multiclass and some multilabel, and show consistent improvement in precision and recall metrics compared to respective baselines. In particular, we train an end-to -end deep classifier on a private product search dataset sampled from Amazon Search Engine with 70 million queries and 49.46 million documents. MACH outperforms, by a significant margin, the state-of-the-art extreme classification models deployed on commercial search engines: Parabel and dense embedding models. Our largest model has 6.4 billion parameters and trains in less than 35 hrs on a single p3.16x machine. Our training times are 7-10x faster, and our memory footprints are 2-4x smaller than the best baselines. This training time is also significantly lower than the one reported by Google’s mixture of experts (MoE) language model on a comparable model size and hardware.

We present FLASH (F ast L SH A lgorithm for S imilarity search accelerated with H PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees.