Breadth-first Search Implementation Research Articles

Fast and efficient parallel breadth-first search with power-law graph transformation

In the big data era, graph computing is widely used to exploit the hidden value in real-world graphs in various scenarios such as social networks, knowledge graphs, web searching, and recommendation systems. However, the random memory accesses result in inefficient use of cache and the irregular degree distribution leads to substantial load imbalance. Breadth-First Search (BFS) is frequently utilized as a kernel for many important and complex graph algorithms. In this paper, we describe a preprocessing approach using Reverse Cuthill-Mckee (RCM) algorithm to improve data locality and demonstrate how to achieve an efficient load balancing for BFS. Computations on RCM-reordered graph data are also accelerated with SIMD executions. We evaluate the performance of the graph preprocessing approach on Kronecker graphs of the Graph500 benchmark and real-world graphs. Our BFS implementation on RCM-reordered graph data achieves 326.48 MTEPS/W (mega TEPS per watt) on an ARMv8 system, ranking 2nd on the Green Graph500 list in June 2020 (the 1st rank uses GPU acceleration).

An efficient parallel algorithm of N-hop neighborhoods on graphs in distributed environment

N-hop neighborhoods information is very useful in analytic tasks on large-scale graphs, like finding clique in a social network, recommending friends or advertising links according to one’s interests, predicting links among websites and etc. To get the N-hop neighborhoods information on a large graph, such as a web graph, a twitter social graph, the most straightforward method is to conduct a breadth first search (BFS) on a parallel distributed graph processing framework, such as Pregel and GraphLab. However, due to the massive volume of message transfer, the BFS method results in high communication cost and has low efficiency. In this work, we propose a key/value based method, namely KVB, which perfectly fits into the prevailing parallel graph processing framework and computes N-hop neighborhoods on a large scale graph efficiently. Unlike the BFS method, our method need not transfer large amount of neighborhoods information, thus, significantly reduces the overhead on both the communication and intermediate results in the distributed framework.We formalize the N-hop neighborhoods query processing as an optimization problem based on a set of quantitative cost metrics of parallel graph processing. Moreover, we propose a solution to efficiently load only the relevant neighborhoods for computation. Specially, we prove the optimal partial neighborhoods load problem is NP-hard and carefully design a heuristic strategy. We have implemented our algorithm on a distributed graph framework- Spark GraphX and validated our solution with extensive experiments over a number of real world and synthetic large graphs on a modest indoor cluster. Experiments show that our solution generally gains an order of magnitude speedup comparing to the state-of-art BFS implementation.

Parallel BFS implementing optimized decomposition of space and kMC simulations for diffusion of vacancies for quantum storage

We present a novel breadth-first search (BFS) algorithm based on the notion of temporal evolvability that is adaptable to various multicore architectures for simulating diffusion of vacancies in hexagonal silicon carbide (4H-SiC) for information storage. The algorithm is formulated in the semi-ring algebraic framework of BFS and incorporates a real-space grid decomposition to optimize the number of nodes that are evaluated in each frontier of the evolution.Scaling characteristics are first evaluated from performance runs for two formulations: (i) recursive depth-first search (DFS) and (ii) semi-ring implementations of BFS. The results for a real-space grid implementation of BFS are then presented. We demonstrate that each new iteration reduces the communication overhead, enhancing performance. A comparison of the real-space grid based BFS with a kinetic Monte Carlo (kMC) algorithm is also presented for the case of diffusion without the influence of the Coulomb interaction. The efficient parallel implementations of this latter approach enables simulations of larger systems than those studied before.

The Implementation of Breadth First Search in Determining of Waris

Breadth First Search is one of the search pattern in an expert system inference mechanism. The use of methods of Breadth First Search in the science of Waris, can be used for the recipient of Waris and the amount of the accepted of Waris. Determination of Waris in this study refers to the madzhab of Hanafi and Hambali. There are three categories of recipient of Waris (Dzawil Furudh, ‘Ashabah, and Dzawil Arham), with 73 rules of Waris and added with 24 rules for heirs who obstructed, which are made in 10 level decision tree of Waris. The test results against 10 cases heirs acquired the suitability and value of the recipient of waris 33 categorized as Dzawil Furudh, and 4 are categorized ‘Ashabah

Space Efficient Linear Time Algorithms for BFS, DFS and Applications

Research on space efficient graph algorithms, particularly for st-connectivity, has a long history including the celebrated polynomial time, O(lg n) bits1 algorithm in undirected graphs by Reingold J. JACM. 55(4) (2008), and polynomial time, \(n/2^{\Theta (\sqrt {\lg n})}\) bits algorithm in directed graphs by Barnes et al. SICOMP. 27(5), 1273–1282 (1998). Recent works by Asano et al. ISAAC (2014) and Elmasry et al. STACS (2015), reconsidered classical fundamental graph algorithms focusing on improving the space complexity. Elmasry et al. gave, among others, an implementation of breadth first search (BFS) in a graph G with n vertices and m edges, taking the optimal O(m + n) time using O(n) bits improving the naive O(n lg n) bits implementation. Similarly, Asano et al. provided space efficient implementations for performing depth first search (DFS) in a graph G. We continue this line of work focusing on improving the space requirement for implementing a few classical graph algorithms. Our first result is a simple data structure that can maintain any subset S of a universe of u elements using just u + o(u) bits and supports in constant time, apart from the standard insert, delete and membership queries, the operation findany that finds and returns any element of the set (or outputs that the set is empty). It can also enumerate all elements present currently in the set in no particular order in O(k + 1) time where k is the number of elements currently belonging to the set. While this data structure supports a weaker set of operations than that of Elmasry et al. STACS (2015), it is simple, more space efficient and is sufficient to support a BFS implementation optimally in O(m + n) time using at most 2n + o(n) bits. Later, we further improve the space requirement of BFS to at most n lg 3 + o(n) bits albeit with a slight increase in running time to O(m lg nf(n)) time where f(n) is any extremely slow growing function of n, and the o term in the space is a function of f(n). We also discuss a similar time-space tradeoff result for finding a minimum weight spanning tree of a weighted (bounded by polynomial in n) undirected graph using n + O(n/f(n)) bits and O(m lg nf(n)) time, for any function f(n) such that 1 ≤ f(n) ≤ n. For DFS in a graph G, we provide an implementation taking O(m + n) time and O(n lg m/n) bits. This partially answers at least for sparse graphs, a question asked by Asano et al. ISAAC (2014) whether DFS can be performed in O (m + n) time and using O(n) bits, and also simultaneously improves the DFS result of Elmasry et al. STACS (2015). Using our DFS algorithm and other careful implementations, we show how one can also test for biconnectivity, 2-edge connectivity, and find cut vertices and bridges of a given undirected graph within the same time and space bounds; earlier classical linear time algorithms for these problems used Ω(n lg n) bits of space.

Enable back memory and global synchronization on LLC buffer

The last-level cache (LLC) shared by heterogeneous processors such as CPU and general-purpose graphics processing unit (GPGPU) brings new opportunities to optimize data sharing among them. Previous work introduces the LLC buffer, which uses part of the LLC storage as a FIFO buffer to enable data sharing between CPU and GPGPU with negligible management overhead. However, the baseline LLC buffer’s capacity is limited and can lead to deadlock when the buffer is full. It also relies on inefficient CPU kernel relaunch and high overhead atomic operations on GPGPU for global synchronization. These limitations motivate us to enable back memory and global synchronization on the baseline LLC buffer and make it more practical. The back memory divides the buffer storage into two levels. While they are managed as a single queue, the data storage in each level is managed as individual circular buffer. The data are redirected to the memory level when the LLC level is full, and are loaded back to the LLC level when it has free space. The case study of n-queen shows that the back memory has a comparative performance with a LLC buffer of infinite LLC level. On the contrary, LLC buffer without back memory exhibits 10% performance degradation incurred by buffer space contention. The global synchronization is enabled by peeking the data about to be read from the buffer. Any request to read the data in LLC buffer after the global barrier is allowed only when all the threads reach the barrier. We adopt breadth-first search (BFS) as a case study and compare the LLC buffer with an optimized implementation of BFS on GPGPU. The results show the LLC buffer has speedup of 1.70 on average. The global synchronization time on GPGPU and CPU is decreased to 38 and 60–5%, respectively.

Large-Scale Graph Processing Analysis using Supercomputer Cluster

Graph implementation is widely use in various sector such as automotive, traffic, image processing and many more. They produce graph in large-scale dimension, cause the processing need long computational time and high specification resources. This research addressed the analysis of implementation large-scale graph using supercomputer cluster. We impelemented graph processing by using Breadth-First Search (BFS) algorithm with single destination shortest path problem. Parallel BFS implementation with Message Passing Interface (MPI) used supercomputer cluster at High Performance Computing Laboratory Computational Science Telkom University and Stanford Large Network Dataset Collection. The result showed that the implementation give the speed up averages more than 30 times and eficiency almost 90%.

Breadth Fixed Gossip: a Route Discovery Mechanism in Ad Hoc Network

The lack of information from a root node to neighbors becomes a particular constraint in a message delivery. While the transmission range of node needs to be considered also for ensuring a delivered packet message to them. Therefore, a route discovery mechanism is a good start to make a reliable path in an unknown environment. The objective of this study is to explore the implementation of Breadth First Search, fixed radius model, and gossip algorithms (Breadth Fixed Gossip) on the ad hoc network. Simulations were conducted to obtain the value of three metrics i.e. saved retransmission, transmission failure, and hop counts. These results were compared with Depth First Search and Gossip performance. It indicates that saved retransmission metric Breadth Fixed Gossip has a 58 times better performance, reduces transmission failure by 20%, and requires 50% more hops at transmission range below 15 than Depth First Search and Gossip.

BFS-4K: An Efficient Implementation of BFS for Kepler GPU Architectures

Breadth-first search (BFS) is one of the most common graph traversal algorithms and the building block for a wide range of graph applications. With the advent of graphics processing units (GPUs), several works have been proposed to accelerate graph algorithms and, in particular, BFS on such many-core architectures. Nevertheless, BFS has proven to be an algorithm for which it is hard to obtain better performance from parallelization. Indeed, the proposed solutions take advantage of the massively parallelism of GPUs but they are often asymptotically less efficient than the fastest CPU implementations. This paper presents BFS-4K , a parallel implementation of BFS for GPUs that exploits the more advanced features of GPU-based platforms (i.e., NVIDIA Kepler) and that achieves an asymptotically optimal work complexity. The paper presents different strategies implemented in BFS-4K to deal with the potential workload imbalance and thread divergence caused by any actual graph non-homogeneity. The paper presents the experimental results conducted on several graphs of different size and characteristics to understand how the proposed techniques are applied and combined to obtain the best performance from the parallel BFS visits. Finally, an analysis of the most representative BFS implementations for GPUs at the state of the art and their comparison with BFS-4K are reported to underline the efficiency of the proposed solution.

Using the Intel Many Integrated Core to accelerate graph traversal

Data-intensive applications have drawn more and more attention in the last few years. The basic graph traversal algorithm, the breadth-first search (BFS), a typical data-intensive application, is widely used and the Graph 500 benchmark uses it to rank the performance of supercomputers. The Intel Many Integrated Core (MIC) architecture, which is designed for highly parallel computing, has not been fully evaluated for graph traversal. In this paper, we discuss how to use the MIC to accelerate the BFS. We present some optimizations for native BFS algorithms and develop a heterogeneous BFS algorithm. For the native BFS algorithm, we mainly discuss how to exploit many cores and wide-vector processing units. The performance of our optimized native BFS implementation is 5.3 times that of the highest published performance for graphics processing units (GPU). For the heterogeneous BFS algorithm, the performance of the general processing unit (CPU) and MIC cooperative computing can gain an increase in speed of approximately 1.4 times than that of a CPU for graphs with 2M vertices. This work is valuable for using a MIC to accelerate the BFS. It is also a general guidance for a MIC used for data-intensive applications.

Exploitation of locality for energy efficiency for breadth first search in fine-grain execution models

In the upcoming exa-scale era, the exploitation of data locality in parallel programs is very important because it benefits both program performance and energy efficiency. However, this is a hard topic for graph algorithms such as the Breadth First Search (BFS) due to the irregular data access patterns. This study analyzes the exploitation of data locality in the BFS and its impact on the energy efficiency with the Codelet fine-grain dataflow-inspired execution model. The Codelet Model more efficiently exploits data locality than the OpenMP-like execution models which traditionally focus on coarse-grain parallelism inside loops. A BFS algorithm is then given to exploit the locality between two loop iterations that belong to two different loops (inter-loop locality). This kind of locality can be exploited by the Codelet Model but not by traditional coarse-grain execution models like OpenMP. Tests were performed on fsim which is a simulation platform developed by Intel for the Ubiquitous High Performance Computing (UHPC) project to design future exa-scale architectures. The results show that this BFS algorithm saves up to 7% of the dynamic energy for memory accesses compared to a BFS implementation based on OpenMP loop scheduling.

A Linear Time Complexity of Breadth-First Search UsingPSystem with Membrane Division

One of the known methods for solving the problems with exponential time complexity such as NP-complete problems is using the brute force algorithms. Recently, a new parallel computational framework called Membrane Computing is introduced which can be applied in brute force algorithms. The usual way to find a solution for the problems with exponential time complexity with Membrane Computing techniques is byPSystem with active membrane using division rule. It makes an exponential workspace and solves the problems with exponential complexity in a polynomial (even linear) time. On the other hand, searching is currently one of the most used methods for finding solution for problems in real life, that the blind search algorithms are accurate, but their time complexity is exponential such as breadth-first search (BFS) algorithm. In this paper, we proposed a new approach for implementation of BFS by usingPsystem with division rule technique for first time. The theorem shows time complexity of BSF in this framework on randomly binary trees reduced fromO(2d)toO(d).