arXiv subjects

Kartik Lakhotia

Publications and source records attributed to Kartik Lakhotia.

14 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

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↗

arXiv2026

PCCL: Process Group-Aware Scalable and Generic Collective Algorithm Synthesizer

Distributed machine learning has become increasingly important due to the massive scale of large-scale generative models. Both model parameters and data are distributed across many compute devices, which requires frequent collective communications to synchronize activations and parameter updates. Such collective communications have become a major bottleneck. While the performance of the collective algorithm depends on the physical network topology, the baseline collective algorithms in collective communication libraries are largely topology-agnostic. Collective algorithm synthesizers address this inefficiency by automatically generating topology-aware collective algorithms. However, prior works have largely overlooked that collective communication typically occurs only among a subset of devices, known as process groups. Additionally, most existing synthesizers are limited in the range of target collective patterns they can generate. We propose PCCL, a scalable and generic framework for synthesizing topology-aware collective algorithms. PCCL is process group-aware and capable of generating near-optimal collective algorithms even when only a subset of devices participates in collective operations. PCCL synthesizes arbitrary collective patterns, including 512-NPU All-to-All synthesis in 11.68 minutes.

cs.DC↗

arXiv2025

Edge-Disjoint Spanning Trees on Star-Product Networks

A star-product operation may be used to create large graphs from smaller factor graphs. Network topologies based on star-products demonstrate several advantages including low-diameter, high scalability, modularity and others. Many state-of-the-art diameter-2 and -3 topologies~(Slim Fly, Bundlefly, PolarStar etc.) can be represented as star products. In this paper, we explore constructions of edge-disjoint spanning trees~(EDSTs) in star-product topologies. EDSTs expose multiple parallel disjoint pathways in the network and can be leveraged to accelerate collective communication, enhance fault tolerance and network recovery, and manage congestion. Our EDSTs have provably maximum or near-maximum cardinality which amplifies their benefits. We further analyze their depths and show that for one of our constructions, all trees have order of the depth of the EDSTs of the factor graphs, and for all other constructions, a large subset of the trees have that depth.

cs.NI↗

arXiv2024

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↗

arXiv2024

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

SPEC2: SPECtral SParsE CNN Accelerator on FPGAs

To accelerate inference of Convolutional Neural Networks (CNNs), various techniques have been proposed to reduce computation redundancy. Converting convolutional layers into frequency domain significantly reduces the computation complexity of the sliding window operations in space domain. On the other hand, weight pruning techniques address the redundancy in model parameters by converting dense convolutional kernels into sparse ones. To obtain high-throughput FPGA implementation, we propose SPEC2 -- the first work to prune and accelerate spectral CNNs. First, we propose a systematic pruning algorithm based on Alternative Direction Method of Multipliers (ADMM). The offline pruning iteratively sets the majority of spectral weights to zero, without using any handcrafted heuristics. Then, we design an optimized pipeline architecture on FPGA that has efficient random access into the sparse kernels and exploits various dimensions of parallelism in convolutional layers. Overall, SPEC2 achieves high inference throughput with extremely low computation complexity and negligible accuracy degradation. We demonstrate SPEC2 by pruning and implementing LeNet and VGG16 on the Xilinx Virtex platform. After pruning 75% of the spectral weights, SPEC2 achieves 0% accuracy loss for LeNet, and <1% accuracy loss for VGG16. The resulting accelerators achieve up to 24x higher throughput, compared with the state-of-the-art FPGA implementations for VGG16.

cs.CV↗

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↗

arXiv2021

Parallel Peeling of Bipartite Networks for Hierarchical Dense Subgraph Discovery

Wing and Tip decomposition construct a hierarchy of butterfly-dense edge and vertex induced bipartite subgraphs, respectively. They have applications in several domains including e-commerce, recommendation systems and document analysis. Existing decomposition algorithms use a bottom-up approach that constructs the hierarchy in an increasing order of subgraph density. They iteratively peel the entities with minimum butterfly count i.e. remove them from the graph and update the butterfly count of other entities. However, the amount of butterflies in large bipartite graphs makes bottom-up peeling computationally demanding. Furthermore, the strict order of peeling entities results in a numerous sequentially dependent iterations, which makes parallelization challenging. In this paper, we propose a novel Parallel Bipartite Network peelinG (PBNG) framework which adopts a two-phased peeling approach to relax the order of peeling, and in turn, reduce synchronization. The first phase divides the decomposition hierarchy into several partitions using very few peeling iterations. The second phase concurrently processes these partitions to generate the final hierarchy, and requires no global synchronization. The two-phased peeling further enables batching optimizations that dramatically improve the computational efficiency. We empirically evaluate PBNG using several real-world bipartite graphs. Compared to the state-of-the-art frameworks and decomposition algorithms, PBNG achieves up to four orders of magnitude reduction in synchronization and two orders of magnitude speedup, respectively. We also present the first decomposition results of some of the largest public real-world datasets, which PBNG can peel in few minutes but existing algorithms fail to process even in several days.

cs.DC↗

arXiv2020

RECEIPT: REfine CoarsE-grained IndePendent Tasks for Parallel Tip decomposition of Bipartite Graphs

Tip decomposition is a crucial kernel for mining dense subgraphs in bipartite networks, with applications in spam detection, analysis of affiliation networks etc. It creates a hierarchy of vertex-induced subgraphs with varying densities determined by the participation of vertices in butterflies (2,2-bicliques). To build the hierarchy, existing algorithms iteratively follow a delete-update(peeling) process: deleting vertices with the minimum number of butterflies and correspondingly updating the butterfly count of their 2-hop neighbors. The need to explore 2-hop neighborhood renders tip-decomposition computationally very expensive. Furthermore, the inherent sequentiality in peeling only minimum butterfly vertices makes derived parallel algorithms prone to heavy synchronization. In this paper, we propose a novel parallel tip-decomposition algorithm -- REfine CoarsE-grained Independent Tasks (RECEIPT) that relaxes the peeling order restrictions by partitioning the vertices into multiple independent subsets that can be concurrently peeled. This enables RECEIPT to simultaneously achieve a high degree of parallelism and dramatic reduction in synchronizations. Further, RECEIPT employs a hybrid peeling strategy along with other optimizations that drastically reduce the amount of wedge exploration and execution time. We perform detailed experimental evaluation of RECEIPT on a shared-memory multicore server. It can process some of the largest publicly available bipartite datasets orders of magnitude faster than the state-of-the-art algorithms -- achieving up to 1100x and 64x reduction in the number of thread synchronizations and traversed wedges, respectively. Using 36 threads, RECEIPT can provide up to 17.1x self-relative speedup. Our implementation of RECEIPT is available at https://github.com/kartiklakhotia/RECEIPT.

cs.DC↗

arXiv2019

Approximation Algorithms for Coordinating Ad Campaigns on Social Networks

We study a natural model of coordinated social ad campaigns over a social network, based on models of Datta et al. and Aslay et al. Multiple advertisers are willing to pay the host - up to a known budget - per user exposure, whether the exposure is sponsored or orgain (i.e. shared by a friend). Campaigns are seeded with sponsored ads to some users, but no user must be exposed to too many sponsored ads. Thus, while ad campaigns proceed independently over the network, they need to be carefully coordinated with respect to their seed sets. We study the objective of maximizing host's total ad revenue. Our main result is to show that under a broad class of influence models, the problem can be reduced to maximizing a submodular function subject to two matroid constraints; it can therefore be approximated within a factor essentially 1/2 in polynomial time. When there is no bound on the individual seed set sizes of advertisers, the constraints correspond only to a single matroid, and the guarantee can be improved to 1-1/e; in that case, a factor 1/2 is achieved by a practical greedy algorithm. The 1-1/e approximation algorithm for matroid-constrained problem is far from practical; however, we show that specifically under the Independent Cascade model, LP rounding and Reverse Reachability techniques can be combined to obtain a 1-1/e approximation algorithm. Our theoretical results are complemented by experiments evaluating the extent to which the coordination of multiple ad campaigns inhibits the revenue obtained from each individual campaign, as a function of the similarity of the influence networks and strength of ties in the networks. Our experiments suggest that as networks for different advertisers become less similar, the harmful effect of competition decreases. With respect to tie strengths, we show that the most harm is done in an intermediate range.

cs.SI↗

arXiv2019

GPOP: A cache- and work-efficient framework for Graph Processing Over Partitions

Past decade has seen the development of many shared-memory graph processing frameworks, intended to reduce the effort of developing high performance parallel applications. However many of these frameworks, based on Vertex-centric or Edge-centric paradigms suffer from several issues, such as poor cache utilization, irregular memory accesses, heavy use of synchronization primitives and theoretical inefficiency, that deteriorate overall performance and scalability. Recently, we proposed a cache and memory efficient partition-centric paradigm for computing PageRank. In this paper, we generalize this approach to develop a novel Graph Processing Over Partitions (GPOP) framework that is cache-efficient, scalable and work-efficient. GPOP induces locality in memory accesses by increasing granularity of execution to vertex subsets called 'partitions', thereby dramatically improving the cache performance of a variety of graph algorithms. It achieves high scalability by enabling completely lock and atomic free computation. GPOP's built-in analytical performance model enables it to use a hybrid of source and partitioncentric communication modes in a way that ensures work-efficiency each iteration, while simultaneously boosting high bandwidth sequential memory accesses. We extensively evaluate the performance of GPOP for a variety of graph algorithms, using several large datasets. We observe that GPOP incurs up to 9x, 6.8x and 5.5x less L2 cache misses compared to Ligra, GraphMat and Galois, respectively. In terms of execution time, GPOP is upto 19x, 9.3x and 3.6x faster than Ligra, GraphMat and Galois respectively.

cs.DC↗

arXiv2019

Planting Trees for scalable and efficient Canonical Hub Labeling

Point-to-Point Shortest Distance (PPSD) query is a crucial primitive in graph database applications. Hub labeling algorithms compute a labeling that converts a PPSD query into a list intersection problem (over a pre-computed indexing) enabling swift query response. However, constructing hub labeling is computationally challenging. Even state-of-the-art parallel algorithms based on Pruned Landmark Labeling (PLL) [3], are plagued by large label size, violation of given network hierarchy, poor scalability and inability to process large graphs. In this paper, we develop novel parallel shared-memory and distributed-memory algorithms for constructing the Canonical Hub Labeling (CHL) that is minimal in size for a given network hierarchy. To the best of our knowledge, none of the existing parallel algorithms guarantee canonical labeling. Our key contribution, the PLaNT algorithm, scales well beyond the limits of current practice by completely avoiding inter-node communication. PLaNT also enables the design of a collaborative label partitioning scheme across multiple nodes for completely in-memory processing of massive graphs whose labels cannot fit on a single machine. Compared to the sequential PLL, we empirically demonstrate upto 47.4x speedup on a 72 thread shared-memory platform. On a 64-node cluster, PLaNT achieves an average 42x speedup over single node execution. Finally, we show how our approach demonstrates superior scalability - we can process 14x larger graphs (in terms of label size) and construct hub labeling orders of magnitude faster compared to state-of-the-art distributed paraPLL algorithm.

cs.DC↗

arXiv2018

Accelerating PageRank using Partition-Centric Processing

PageRank is a fundamental link analysis algorithm that also functions as a key representative of the performance of Sparse Matrix-Vector (SpMV) multiplication. The traditional PageRank implementation generates fine granularity random memory accesses resulting in large amount of wasteful DRAM traffic and poor bandwidth utilization. In this paper, we present a novel Partition-Centric Processing Methodology (PCPM) to compute PageRank, that drastically reduces the amount of DRAM communication while achieving high sustained memory bandwidth. PCPM uses a Partition-centric abstraction coupled with the Gather-Apply-Scatter (GAS) programming model. By carefully examining how a PCPM based implementation impacts communication characteristics of the algorithm, we propose several system optimizations that improve the execution time substantially. More specifically, we develop (1) a new data layout that significantly reduces communication and random DRAM accesses, and (2) branch avoidance mechanisms to get rid of unpredictable data-dependent branches. We perform detailed analytical and experimental evaluation of our approach using 6 large graphs and demonstrate an average 2.7x speedup in execution time and 1.7x reduction in communication volume, compared to the state-of-the-art. We also show that unlike other GAS based implementations, PCPM is able to further reduce main memory traffic by taking advantage of intelligent node labeling that enhances locality. Although we use PageRank as the target application in this paper, our approach can be applied to generic SpMV computation.

cs.DC↗