Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.12457

A Block-Based Triangle Counting Algorithm on Heterogeneous Environments

Abdurrahman Yaşar·Sivasankaran Rajamanickam·Jonathan Berry·Ümit V. Çatalyürek
View original source ↗Read source document ↗Export metadata ↓

Abstract

Triangle counting is a fundamental building block in graph algorithms. In this paper, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Abdurrahman Yaşar, Sivasankaran Rajamanickam, Jonathan Berry, Ümit V. Çatalyürek. 2020-09-25. A Block-Based Triangle Counting Algorithm on Heterogeneous Environments. https://arxiv.org/abs/2009.12457

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗