arXiv subjects

Fabrizio Petrini

Publications and source records attributed to Fabrizio Petrini.

At least 19 recordsLinked to original sources

arXiv2026

Kronecker Products, Polarity Quotients and Large Graph Constructions

In this paper, we establish a structural compatibility between the Kronecker product of bipartite graphs that admit polarity and their polarity quotient, and provide a sharp upper bound on the diameter of these graphs. For certain factor graphs, the diameter of the Kronecker product meets the upper bound on diameter, among them the generalized polygons. Generalized polygons with their polarity quotients have been notably used in the past to construct very large graphs. We apply the structural theorems in the paper to generalized polygons $\mathbb{G}_n(q,q)$ used as factor graphs, and build three new families of graphs of large order covering an infinite but sparse set of degrees, one of diameter $2$, one of diameter $3$ and one of diameter $5$. These asymptotically approach a theoretical upper bound on graph size as orders $q$ and $r$ of the generalized polygon factors increase. As an example, we develop one such family, derived from generalized quadrangles, and construct new diameter-$3$ graphs of low degree that are larger than any previously known at their degrees.

math.CO↗

arXiv2026

$g$MAGNUS: Fast SpGEMM on GPUs for Irregular Matrices via Hierarchical Multisplit

We present $g$MAGNUS, a novel algorithm for sparse matrix-matrix multiplication (SpGEMM) of irregular matrices on GPUs. Such matrices often contain many heavy rows, those with large intermediate products that force local memory accumulators to spill to global memory. $g$MAGNUS addresses this by computing an intra-row reordering of intermediate products, subdividing heavy rows into independent chunks that can be accumulated completely in local memory. This reordering uses novel outer product and hierarchical multisplit operations. The algorithm is input- and system-aware, automatically determining the number of chunks and multisplit levels based on the input matrix dimensions and local memory size. Experimental results on two extensive datasets show that $g$MAGNUS achieves a geometric-mean speedup of 1.81 to 7.62$\times$ over five leading algorithms (including MKL and cuSPARSE) on Intel Ponte Vecchio and NVIDIA H200. Additionally, the core kernels of $g$MAGNUS are evaluated, achieving near-peak performance compared to their theoretical upper bound.

cs.DC↗

arXiv2025

ReLATE: Accelerating Tensor Decomposition via Safe and Efficient Learning of Sparse Encodings

Tensor decomposition (TD) is essential for analyzing high-dimensional sparse data, yet its irregular computations and memory-access patterns pose major performance challenges on modern parallel processors. Prior works rely on expert-designed sparse tensor formats that fail to adapt to irregular tensor shapes and data distributions. We present the reinforcement-learned adaptive tensor encoding (ReLATE) framework, a learning-augmented method that discovers safe and efficient sparse encodings, without labeled examples, via a hybrid model-free and model-based algorithm that learns from both real and imagined actions. Moreover, ReLATE introduces elastic training, rule-driven action masking, and dynamics-informed action filtering to ensure correct encoding with bounded execution time, even during early learning. After offline training, with geometric-mean overhead of only 5.82% relative to TD workflow time, ReLATE deploys the best encoding with zero inference overhead. Across diverse real-world sparse tensors, ReLATE consistently outperforms the best expert-designed format by up to 2x, with a geometric-mean speedup of 1.38-1.41x.

cs.LG↗

arXiv2025

Scaling Intelligence: Designing Data Centers for Next-Gen Language Models

The explosive growth of Large Language Models (LLMs), such as GPT-4 with 1.8 trillion parameters, demands a fundamental rethinking of data center architecture to ensure scalability, efficiency, and cost-effectiveness. Our work provides a comprehensive co-design framework that jointly explores FLOPS, HBM bandwidth and capacity, multiple network topologies (two-tier vs. FullFlat optical), the size of the scale-out domain, and popular parallelism/optimization strategies used in LLMs. We introduce and evaluate FullFlat network architectures, which provide uniform high-bandwidth, low-latency connectivity between all nodes, and demonstrate their transformative impact on performance and scalability. Through detailed sensitivity analyses, we quantify the benefits of overlapping compute and communication, leveraging hardware-accelerated collectives, widening the scale-out domain, and increasing memory capacity. Our study spans both sparse (mixture of experts) and dense transformer-based LLMs, revealing how system design choices affect Model FLOPS Utilization (MFU = Model FLOPS per token * Observed tokens per second / Peak FLOPS of the hardware) and overall throughput. For the co-design study, we utilized an analytical performance modeling tool capable of predicting LLM runtime within 10% of real-world measurements. Our findings offer actionable insights and a practical roadmap for designing AI data centers that can efficiently support trillion-parameter models, reduce optimization complexity, and sustain the rapid evolution of AI capabilities.

cs.AR↗

arXiv2025

MAGNUS: Generating Data Locality to Accelerate Sparse Matrix-Matrix Multiplication on CPUs

Sparse general matrix-matrix multiplication (SpGEMM) is a critical operation in many applications. Current multithreaded implementations are based on Gustavson's algorithm and often perform poorly on large matrices due to limited cache reuse by the accumulators. We present MAGNUS (Matrix Algebra for Gigantic NUmerical Systems), a novel algorithm to maximize data locality in SpGEMM. To generate locality, MAGNUS reorders the intermediate product into discrete cache-friendly chunks using a two-level hierarchical approach. The accumulator is applied to each chunk, where the chunk size is chosen such that the accumulator is cache-efficient. MAGNUS is input- and system-aware: based on the matrix characteristics and target system specifications, the optimal number of chunks is computed by minimizing the storage cost of the necessary data structures. MAGNUS allows for a hybrid accumulation strategy in which each chunk uses a different accumulator based on an input threshold. We consider two accumulators: an AVX-512 vectorized bitonic sorting algorithm and classical dense accumulation. An OpenMP implementation of MAGNUS is compared with several baselines, including Intel MKL, for a variety of different matrices on three Intel architectures. For matrices from the SuiteSparse collection, MAGNUS is faster than all the baselines in most cases and is often an order of magnitude faster than at least one baseline. For massive random matrices, MAGNUS scales to the largest matrix sizes, while the baselines do not. Furthermore, MAGNUS is close to the optimal bound for these matrices, regardless of the matrix size, structure, and density.

cs.DC↗

arXiv2024

Enhancing Scalability and Performance in Influence Maximization with Optimized Parallel Processing

Influence Maximization (IM) is vital in viral marketing and biological network analysis for identifying key influencers. Given its NP-hard nature, approximate solutions are employed. This paper addresses scalability challenges in scale-out shared memory system by focusing on the state-of-the-art Influence Maximization via Martingales (IMM) benchmark. To enhance the work efficiency of the current IMM implementation, we propose EFFICIENTIMM with key strategies, including new parallelization scheme, NUMA-aware memory usage, dynamic load balancing and fine-grained adaptive data structures. Benchmarking on a 128-core CPU system with 8 NUMA nodes, EFFICIENTIMM demonstrated significant performance improvements, achieving an average 5.9x speedup over Ripples across 8 diverse SNAP datasets, when compared to the best execution times of the original Ripples framework. Additionally, on the Youtube graph, EFFICIENTIMM demonstrates a better memory access pattern with 357.4x reduction in L1+L2 cache misses as compared to Ripples.

cs.DC↗

arXiv2024

Efficient Parallel Multi-Hop Reasoning: A Scalable Approach for Knowledge Graph Analysis

Multi-hop reasoning (MHR) is a process in artificial intelligence and natural language processing where a system needs to make multiple inferential steps to arrive at a conclusion or answer. In the context of knowledge graphs or databases, it involves traversing multiple linked entities and relationships to understand complex queries or perform tasks requiring a deeper understanding. Multi-hop reasoning is a critical function in various applications, including question answering, knowledge base completion, and link prediction. It has garnered significant interest in artificial intelligence, machine learning, and graph analytics. This paper focuses on optimizing MHR for time efficiency on large-scale graphs, diverging from the traditional emphasis on accuracy which is an orthogonal goal. We introduce a novel parallel algorithm that harnesses domain-specific learned embeddings to efficiently identify the top K paths between vertices in a knowledge graph to find the best answers to a three-hop query. Our contributions are: (1) We present a new parallel algorithm to enhance MHR performance, scalability and efficiency. (2) We demonstrate the algorithm's superior performance on leading-edge Intel and AMD architectures through empirical results. We showcase the algorithm's practicality through a case study on identifying academic affiliations of potential Turing Award laureates in Deep Learning, highlighting its capability to handle intricate entity relationships. This demonstrates the potential of our approach to enabling high-performance MHR, useful to navigate the growing complexity of modern knowledge graphs.

cs.AI↗

arXiv2024

Accelerating Sparse Tensor Decomposition Using Adaptive Linearized Representation

High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis tools based on tensor decomposition (TD) methods. However, real-world sparse tensors exhibit highly irregular shapes and data distributions, which pose significant challenges for making efficient use of modern parallel processors. This study breaks the prevailing assumption that compressing sparse tensors into coarse-grained structures or along a particular dimension/mode is more efficient than keeping them in a fine-grained, mode-agnostic form. Our novel sparse tensor representation, Adaptive Linearized Tensor Order (ALTO), encodes tensors in a compact format that can be easily streamed from memory and is amenable to both caching and parallel execution. In contrast to existing compressed tensor formats, ALTO constructs one tensor copy that is agnostic to both the mode orientation and the irregular distribution of nonzero elements. To demonstrate the efficacy of ALTO, we propose a set of parallel TD algorithms that exploit the inherent data reuse of tensor computations to substantially reduce synchronization overhead, decrease memory footprint, and improve parallel performance. Additionally, we characterize the major execution bottlenecks of TD methods on the latest Intel Xeon Scalable processors and introduce dynamic adaptation heuristics to automatically select the best algorithm based on the sparse tensor characteristics. Across a diverse set of real-world data sets, ALTO outperforms the state-of-the-art approaches, achieving more than an order-of-magnitude speedup over the best mode-agnostic formats. Compared to the best mode-specific formats, ALTO achieves 5.1X geometric mean speedup at a fraction (25%) of their storage costs.

cs.DC↗

arXiv2023

Open Problems in (Hyper)Graph Decomposition

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final application concerns a different problem (such as traversal, finding paths, trees, and flows), decomposing large graphs is often an important subproblem for complexity reduction or parallelization. This report is a summary of discussions that happened at Dagstuhl seminar 23331 on "Recent Trends in Graph Decomposition" and presents currently open problems and future directions in the area of (hyper)graph decomposition.

cs.DS↗

arXiv2023

A High-Performance Design, Implementation, Deployment, and Evaluation of The Slim Fly Network

Novel low-diameter network topologies such as Slim Fly (SF) offer significant cost and power advantages over the established Fat Tree, Clos, or Dragonfly. To spearhead the adoption of low-diameter networks, we design, implement, deploy, and evaluate the first real-world SF installation. We focus on deployment, management, and operational aspects of our test cluster with 200 servers and carefully analyze performance. We demonstrate techniques for simple cabling and cabling validation as well as a novel high-performance routing architecture for InfiniBand-based low-diameter topologies. Our real-world benchmarks show SF's strong performance for many modern workloads such as deep neural network training, graph analytics, or linear algebra kernels. SF outperforms non-blocking Fat Trees in scalability while offering comparable or better performance and lower cost for large network sizes. Our work can facilitate deploying SF while the associated (open-source) routing architecture is fully portable and applicable to accelerate any low-diameter interconnect.

cs.NI↗

arXiv2023

PolarFly: A Cost-Effective and Flexible Low-Diameter Topology

In this paper we present PolarFly, a diameter-2 network topology based on the Erdos-Renyi family of polarity graphs from finite geometry. This is a highly scalable low-diameter topology that asymptotically reaches the Moore bound on the number of nodes for a given network degree and diameter PolarFly achieves high Moore bound efficiency even for the moderate radixes commonly seen in current and near-future routers, reaching more than 96% of the theoretical peak. It also offers more feasible router degrees than the state-of-the-art solutions, greatly adding to the selection of scalable diameter-2 networks. PolarFly enjoys many other topological properties highly relevant in practice, such as a modular design and expandability that allow incremental growth in network size without rewiring the whole network. Our evaluation shows that PolarFly outperforms competitive networks in terms of scalability, cost and performance for various traffic patterns.

cs.NI↗

arXiv2023

PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks

We present PolarStar, a novel family of diameter-3 network topologies derived from the star product of low-diameter factor graphs. PolarStar gives the largest known diameter-3 network topologies for almost all radixes, thus providing the best known scalable diameter-$3$ network. Compared to current state-of-the-art diameter-$3$ networks, PolarStar achieves $1.3\times$ geometric mean increase in scale over Bundlefly, $1.9\times$ over Dragonfly, and $6.7\times$ over {3-D} HyperX. PolarStar has many other desirable properties, including a modular layout, large bisection, high resilience to link failures and a large number of feasible configurations for every radix. We give a detailed evaluation with simulations of synthetic and real-world traffic patterns and show that PolarStar exhibits comparable or better performance than current diameter-3 networks.

cs.NI↗

arXiv2022

Ridgeline: A 2D Roofline Model for Distributed Systems

In this short paper, we introduce the Ridgeline model, an extension of the Roofline model [4] for distributed systems. The Roofline model targets shared memory systems, bounding the performance of a kernel based on its operational intensity, and the peak compute throughput and memory bandwidth of the execution system. In a distributed setting, with multiple communicating compute entities, the network must be taken into account to model the system behavior accurately. The Ridgeline aggregates information on compute, memory, and network limits in one 2D plot to show, in an intuitive way, which of the resources is the expected bottleneck. We show the applicability of the Ridgeline in a case study based on a data-parallel Multi-Layer Perceptron (MLP) instance.

cs.DC↗

arXiv2022

Efficient, Out-of-Memory Sparse MTTKRP on Massively Parallel Architectures

Tensor decomposition (TD) is an important method for extracting latent information from high-dimensional (multi-modal) sparse data. This study presents a novel framework for accelerating fundamental TD operations on massively parallel GPU architectures. In contrast to prior work, the proposed Blocked Linearized Coordinate (BLCO) format enables efficient out-of-memory computation of tensor algorithms using a unified implementation that works on a single tensor copy. Our adaptive blocking and linearization strategies not only meet the resource constraints of GPU devices, but also accelerate data indexing, eliminate control-flow and memory-access irregularities, and reduce kernel launching overhead. To address the substantial synchronization cost on GPUs, we introduce an opportunistic conflict resolution algorithm, in which threads collaborate instead of contending on memory access to discover and resolve their conflicting updates on-the-fly, without keeping any auxiliary information or storing non-zero elements in specific mode orientations. As a result, our framework delivers superior in-memory performance compared to prior state-of-the-art, and is the only framework capable of processing out-of-memory tensors. On the latest Intel and NVIDIA GPUs, BLCO achieves 2.12-2.6X geometric-mean speedup (with up to 33.35X speedup) over the state-of-the-art mixed-mode compressed sparse fiber (MM-CSF) on a range of real-world sparse tensors.

cs.DC↗

arXiv2022

A New Parallel Algorithm for Sinkhorn Word-Movers Distance and Its Performance on PIUMA and Xeon CPU

The Word Movers Distance (WMD) measures the semantic dissimilarity between two text documents by computing the cost of optimally moving all words of a source/query document to the most similar words of a target document. Computing WMD between two documents is costly because it requires solving an $O(V^3log(V))$ optimization problem where $V$ is the number of unique words in the document. Fortunately, WMD can be framed as an Earth Mover's Distance (EMD) for which the algorithmic complexity can be reduced to $O(V^2)$ by adding an entropy penalty to the optimization problem and solving it using the Sinkhorn-Knopp algorithm. Additionally, the computation can be made highly parallel by adopting a batching approach, i.e., computing the WMD of a single query document against multiple target documents at once. Sinkhorn WMD is a key kernel used in many ML/NLP applications. and usually gets implemented in Python. However, a straightforward Python implementation may leave significant performance on the table even though it may internally call optimized C++ BLAS routines. We present a new sparse {P}arallel {A}lgorithm for {S}inkhorn-Knopp {W}ord-movers {D}istance to compute the semantic distance of one document to many other documents by adopting the $O(V^2)$ EMD algorithm. We algorithmically transform $O(V^2)$ dense compute-heavy EMD version into an equivalent sparse one using new fused SDDMM-SpMM (sparse selection of dense-dense matrix-, sparse-dense matrix-multiplication) kernels. We implemented and optimized this algorithm for two very different architectures -- the new Intel Programmable Integrated Unified Memory Architecture (PIUMA) and Intel Xeon CPUs. We show that we were able to reach close to peak performance on both platforms.

cs.DC↗

arXiv2021

EvalNet: A Practical Toolchain for Generation and Analysis of Extreme-Scale Interconnects

The diversity of communication paths in a network, especially non-minimal paths, is a key enabler of performance at extreme scales. We present EvalNet, a toolchain for scalable generation and analysis of over 25 important network topologies, such as Slim Fly, PolarFly, and Orthogonal Fat Trees, with a strong focus on path diversity metrics. EvalNet provides an extensive and fine-grained analysis of shortest and non-shortest paths, including their multiplicities, lengths, and interference. It supports exact measurement and visualization of bandwidth and throughput between every router pair, enabling unprecedented insight into routing potential. EvalNet also includes detailed models for construction cost and power consumption, and interfaces seamlessly with established simulators, which we tune to support large-scale evaluations on low-cost hardware. Using EvalNet, we deliver the widest and most comprehensive path diversity study to date, demonstrating how path diversity underpins throughput and scalability, and facilitating progress towards new frontiers in extreme-scale network design.

cs.NI↗

arXiv2021

ALTO: Adaptive Linearized Storage of Sparse Tensors

The analysis of high-dimensional sparse data is becoming increasingly popular in many important domains. However, real-world sparse tensors are challenging to process due to their irregular shapes and data distributions. We propose the Adaptive Linearized Tensor Order (ALTO) format, a novel mode-agnostic (general) representation that keeps neighboring nonzero elements in the multi-dimensional space close to each other in memory. To generate the indexing metadata, ALTO uses an adaptive bit encoding scheme that trades off index computations for lower memory usage and more effective use of memory bandwidth. Moreover, by decoupling its sparse representation from the irregular spatial distribution of nonzero elements, ALTO eliminates the workload imbalance and greatly reduces the synchronization overhead of tensor computations. As a result, the parallel performance of ALTO-based tensor operations becomes a function of their inherent data reuse. On a gamut of tensor datasets, ALTO outperforms an oracle that selects the best state-of-the-art format for each dataset, when used in key tensor decomposition operations. Specifically, ALTO achieves a geometric mean speedup of 8X over the best mode-agnostic (coordinate and hierarchical coordinate) formats, while delivering a geometric mean compression ratio of 4.3X relative to the best mode-specific (compressed sparse fiber) formats.

cs.DC↗

arXiv2021

Online and Real-time Object Tracking Algorithm with Extremely Small Matrices

Online and Real-time Object Tracking is an interesting workload that can be used to track objects (e.g., car, human, animal) in a series of video sequences in real-time. For simple object tracking on edge devices, the output of object tracking could be as simple as drawing a bounding box around a detected object and in some cases, the input matrices used in such computation are quite small (e.g., 4x7, 3x3, 5x5, etc). As a result, the amount of actual work is low. Therefore, a typical multi-threading based parallelization technique can not accelerate the tracking application; instead, a throughput based parallelization technique where each thread operates on independent video sequences is more rewarding. In this paper, we share our experience in parallelizing a Simple Online and Real-time Tracking (SORT) application on shared-memory multicores.

cs.DC↗