Average shortest path length of graphs of diameter 3

Mori, Ryusaburo

doi:10.1109/nocs.2016.7579335

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…The exhaustive computer search of an optimal graph of fixed size and degree is computationally expensive, e.g., the number of non-isomorphic 32-vertex degree-3 regular graphs, labeled as (32,3), is ~10 13 [34]. Thus, heuristics have been developed using greedy local search [35], simulated annealing [36], or theoretical graph product and construction [37] for reduced search duration.…”

Section: Discovery Of Optimal Network Topologiesmentioning

confidence: 99%

Optimal low-latency network topologies for cluster performance enhancement

et al. 2020

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We propose that clusters interconnected with network topologies having minimal mean path length will increase their overall performance for a variety of applications. We approach our heuristic by constructing clusters of up to 36 nodes having Dragonfly, torus, ring, Chvatal, Wagner, Bidiakis and several other topologies with minimal mean path lengths and by simulating the performance of 256-node clusters with the same network topologies. The optimal (or sub-optimal) low-latency network topologies are found by minimizing the mean path length of regular graphs. The selected topologies are benchmarked using pingpong messaging, the MPI collective communications, and the standard parallel applications including effective bandwidth, FFTE, Graph 500 and NAS parallel benchmarks. We established strong correlations between the clusters' performances and the network topologies, especially the mean path lengths, for a wide range of applications. In communication-intensive benchmarks, clusters with optimal network topologies out-perform those with mainstream topologies by several folds. It is striking that a mere adjustment of the network topology suffices to reclaim performance from the same computing hardware.

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Section: Discovery Of Optimal Network Topologiesmentioning

confidence: 99%

Optimal low-latency network topologies for cluster performance enhancement

et al. 2020

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“…The official website publishes some slides and papers on methods developed by past participants [17,19,24]. The methods can be broadly divided into two groups.…”

Section: Related Work 21 Order/degree Problemmentioning

confidence: 99%

“…Although the definition of the order/degree problem is simple, no efficient method for solving it has thus far been found. For this reason, metaheuristic algorithms such as simulated annealing (SA) [7,9] are often used [13,16,17]. However, metaheuristic algorithms require many calculations to obtain the solution for the current state of a system.…”

Section: Introductionmentioning

confidence: 99%

Parallelization of All-Pairs-Shortest-Path Algorithms in Unweighted Graph

Nakao

Murai

Sato

2020

Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region

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The design of the network topology of a large-scale parallel computer system can be represented as an order/degree problem in graph theory. To solve the order/degree problem, it is necessary to obtain an all-pairs-shortest-path (APSP) of the graph. Thus, this paper evaluates two parallel algorithms that quickly find the APSP in unweighted graphs and compares their performance. The first APSP algorithm is based on the breadth-first search (BFS-APSP) and the second is based on the adjacency matrix (ADJ-APSP). First, we develop serial algorithms and threaded algorithms using OpenMP, and show that ADJ-APSP is up to 32.34 times faster than BFS-APSP. Next, we develop hybrid-parallel algorithms using OpenMP and MPI, and show that BFS-APSP is faster than ADJ-APSP under certain conditions because the maximum number of processes in BFS-APSP is greater than in ADJ-APSP. In addition, we parallelize ADJ-APSP using a single GPU (NVIDIA Tesla V100) and achieve a speed increase of up to 16.53-fold compared to that of a single CPU. Finally, we evaluate the performance of the algorithms using 128 GPUs and achieve a computation time 101.10 times faster than that using a single GPU. Moreover, it is shown that the calculation time of both algorithms can be greatly reduced when the input graphs are symmetric. CCS CONCEPTS • Theory of computation → Massively parallel algorithms.

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“…The Graph Golf official website [13] links to several slides and papers by past participants [15,16,19]. Existing methods can be classified into the following two categories.…”

Section: Related Workmentioning

confidence: 99%

“…Although this method requires almost no computation for the APSP problem, only graphs with specific numbers of vertices and degrees can be created. (2) Based on a random graph, a target graph with the smallest diameter and ASPL is created using an optimization method such as SA [15]. Although this method can create graphs with arbitrary numbers of vertices and degrees, since an enormous number of calculations for the APSP problem is necessary, approximation is often used.…”

Section: Related Workmentioning

confidence: 99%

A Method for Order/Degree Problem Based on Graph Symmetry and Simulated Annealing with MPI/OpenMP Parallelization

Nakao

Murai

Sato

2019

Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region

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The network topology in various systems, such as large-scale data centers, high-performance computing systems, and Network on Chip, is strongly related to network latency. Designing a network topology with low latency can be defined as an order/degree problem (ODP) in graph theory by modeling the network topology as an undirected graph. This study proposes a method for efficiently solving ODPs based on graph symmetry and simulated annealing (SA). This method makes the network topology symmetrical, thereby improving the solution search performance of SA and drastically reducing the calculation time. The proposed method is applied to several problems from an international competition for ODPs called Graph Golf to find network topologies with sufficiently low latency. The symmetry-based calculation achieves a speed up of 31.76 times for one of the problems. Furthermore, to reduce calculation time, the proposed method is extended to use hybrid parallelization with MPI and OpenMP. As a result, a maximum speed up of 209.80 times was achieved on 20 compute nodes consisting of 400 CPU cores. Even faster performance was achieved by combining the symmetry-based calculation and hybrid parallelization. CCS CONCEPTS • Networks → Topology analysis and generation;

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Average shortest path length of graphs of diameter 3

Cited by 9 publications

References 10 publications

Optimal low-latency network topologies for cluster performance enhancement

Optimal low-latency network topologies for cluster performance enhancement

Parallelization of All-Pairs-Shortest-Path Algorithms in Unweighted Graph

A Method for Order/Degree Problem Based on Graph Symmetry and Simulated Annealing with MPI/OpenMP Parallelization

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