scholarly journals Graph Connectivity in Log Steps Using Label Propagation

2021 ◽  
Author(s):  
Paul Burkhardt
Keyword(s):  
Computational Models ◽  
Undirected Graph ◽  
Random Access ◽  
Memory Systems ◽  
Label Propagation ◽  
Graph Connectivity ◽  
Connected Components ◽  
Original Graph ◽  
Path Graph ◽  
Parallel Random Access Machine

The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a Parallel Random Access Machine (PRAM). These algorithms maintain a spanning forest by merging and compressing trees, which requires pointer-chasing operations that increase memory access latency and are limited to shared-memory systems. Many of these PRAM algorithms are also very complicated to implement. Another popular method is “leader-contraction” where the challenge is to select a constant fraction of leaders that are adjacent to a constant fraction of non-leaders with high probability, but this can require adding more edges than were in the original graph. Instead we investigate label propagation because it is deterministic, easy to implement, and does not rely on pointer-chasing. Label propagation exchanges representative labels within a component using simple graph traversal, but it is inherently difficult to complete in a sublinear number of steps. We are able to overcome the problems with label propagation for graph connectivity. We introduce a surprisingly simple framework for deterministic, undirected graph connectivity using label propagation that is easily adaptable to many computational models. It achieves logarithmic convergence independently of the number of processors and without increasing the edge count. We employ a novel method of propagating directed edges in alternating direction while performing minimum reduction on vertex labels. We present new algorithms in PRAM, Stream, and MapReduce. Given a simple, undirected graph [Formula: see text] with [Formula: see text] vertices, [Formula: see text] edges, our approach takes O(m) work each step, but we can only prove logarithmic convergence on a path graph. It was conjectured by Liu and Tarjan (2019) to take [Formula: see text] steps or possibly [Formula: see text] steps. Our experiments on a range of difficult graphs also suggest logarithmic convergence. We leave the proof of convergence as an open problem.

Transforming comparison model lower bounds to the parallel-random-access-machine

1997 ◽  
Vol 62 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Dany Breslauer ◽  
Artur Czumaj ◽  
Devdatt P. Dubhashi ◽  
Friedhelm Meyer auf der Heide
Keyword(s):  
Lower Bounds ◽  
Random Access ◽  
Comparison Model ◽  
Random Access Machine ◽  
Parallel Random Access Machine

scholarly journals ConnectIt

2020 ◽  
Vol 14 (4) ◽  
pp. 653-667
Author(s):  
Laxman Dhulipala ◽  
Changwan Hong ◽  
Julian Shun
Keyword(s):  
Experimental Evaluation ◽  
Comprehensive Evaluation ◽  
State Of The Art ◽  
Graph Connectivity ◽  
Connected Components ◽  
Sampling Strategies ◽  
Spanning Forest ◽  
Speed Up ◽  
Minimum Spanning Forest ◽  
Edge Sampling

Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.

PARALLEL ALGORITHMS FOR SOME DOMINANCE PROBLEMS BASED ON THE PRAM MODEL

1993 ◽  
Vol 03 (04) ◽  
pp. 367-382
Author(s):  
I.W. CHAN ◽  
D.K. FRIESEN
Keyword(s):  
Computational Model ◽  
Single Point ◽  
Random Access ◽  
Geometric Algorithms ◽  
Counting Problem ◽  
Erew Pram ◽  
Pram Model ◽  
Input Size ◽  
Parallel Random Access Machine ◽  
Direct Dominance

Two parallel geometric algorithms based on the idea of point domination are presented. The first algorithm solves the d-dimensional isothetic rectangles intersection counting problem of input size N/2d, where d>1 and N is a multiple of 2d, in O( log d−1 N) time and O(N log N) space. The second algorithm solves the direct dominance reporting problem for a set of N points in the plane in O( log N+J) time and O(N log N) space, where J denotes the maximum of the number of direct dominances reported by any single point in the set. Both algorithms make use of the EREW PRAM (Exclusive Read Exclusive Write Parallel Random Access Machine) consisting of O(N) processors as the computational model.

scholarly journals Q-Selector-Based Prefetching Method for DRAM/NVM Hybrid Main Memory System

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2158
Author(s):  
Jeong-Geun Kim ◽  
Shin-Dug Kim ◽  
Su-Kyung Yoon
Keyword(s):  
Performance Status ◽  
Random Access ◽  
Memory Systems ◽  
Memory System ◽  
Main Memory ◽  
Learning Method ◽  
Q Learning ◽  
Data Intensive ◽  
Big Data Applications ◽  
Non Volatile Memory

This research is to design a Q-selector-based prefetching method for a dynamic random-access memory (DRAM)/ Phase-change memory (PCM)hybrid main memory system for memory-intensive big data applications generating irregular memory accessing streams. Specifically, the proposed method fully exploits the advantages of two-level hybrid memory systems, constructed as DRAM devices and non-volatile memory (NVM) devices. The Q-selector-based prefetching method is based on the Q-learning method, one of the reinforcement learning algorithms, which determines a near-optimal prefetcher for an application’s current running phase. For this, our model analyzes real-time performance status to set the criteria for the Q-learning method. We evaluate the Q-selector-based prefetching method with workloads from data mining and data-intensive benchmark applications, PARSEC-3.0 and graphBIG. Our evaluation results show that the system achieves approximately 31% performance improvement and increases the hit ratio of the DRAM-cache layer by 46% on average compared to a PCM-only main memory system. In addition, it achieves better performance results compared to the state-of-the-art prefetcher, access map pattern matching (AMPM) prefetcher, by 14.3% reduction of execution time and 12.89% of better CPI enhancement.

scholarly journals Thinning a Triangulation of a Bayesian Network or Undirected Graph to Create a Minimal Triangulation

2017 ◽  
Vol 25 (03) ◽  
pp. 1750014
Author(s):  
Edmund Jones ◽  
Vanessa Didelez
Keyword(s):  
Bayesian Network ◽  
Graphical Model ◽  
Undirected Graph ◽  
Computer Experiment ◽  
R Package ◽  
The Other ◽  
Prime Decomposition ◽  
Original Graph ◽  
Minimal Triangulation

In one procedure for finding the maximal prime decomposition of a Bayesian network or undirected graphical model, the first step is to create a minimal triangulation of the network, and a common and straightforward way to do this is to create a triangulation that is not necessarily minimal and then thin this triangulation by removing excess edges. We show that the algorithm for thinning proposed in several previous publications is incorrect. A different version of this algorithm is available in the R package gRbase, but its correctness has not previously been proved. We prove that this version is correct and provide a simpler version, also with a proof. We compare the speed of the two corrected algorithms in three ways and find that asymptotically their speeds are the same, neither algorithm is consistently faster than the other, and in a computer experiment the algorithm used by gRbase is faster when the original graph is large, dense, and undirected, but usually slightly slower when it is directed.

Sign in / Sign up

Export Citation Format

Share Document