Multilevel Graph Partitioning Algorithm Research Articles

A massively parallel implicit 3D unstructured grid solver for computing turbulent flows on latest distributed memory computational architectures

An implicit unstructured grid density-based solver–PRAVAHA based on a parallel variant of the lower upper symmetric Gauss-Seidel (LUSGS) method is developed to compute large-scale engineering problems. A four-layered parallel algorithm is designed to efficiently compute three-dimensional turbulent flows on massively parallel modern multiple instruction multiple data-stream (MIMD) computational hardware. This data parallel approach achieves multiple layers of parallelism including continuity of flow solution, transfer of solution gradients, and calculation of drag/lift/solution residuals, right up to the innermost implicit LUSGS solver sub-routine, which is relatively less explored in the literature. Domain decomposition is performed using the METIS software based on multi-level graph partitioning algorithms. Non-blocking message-passing interface library functions are used to manage inter-processor communication through explicit message passing, efficiently. Super-linear scalability of the parallel solver is established on the current state-of-the-art supercomputing facility, the 838 teraflops PARAM seva on up to 6144 cores. Linear or even super-linear speedup on problems of significant size is observed even on ad-hoc parallel computing platforms like workstations and multi-node clusters, for turbulent flow simulations.

Load Balancing Based on Firefly and Ant Colony Optimization Algorithms for Parallel Computing.

With the wide application of computational fluid dynamics in various fields and the continuous growth of the complexity of the problem and the scale of the computational grid, large-scale parallel computing came into being and became an indispensable means to solve this problem. In the numerical simulation of multi-block grids, the mapping strategy from grid block to processor is an important factor affecting the efficiency of load balancing and communication overhead. The multi-level graph partitioning algorithm is an important algorithm that introduces graph network dynamic programming to solve the load-balancing problem. This paper proposed a firefly-ant compound optimization (FaCO) algorithm for the weighted fusion of two optimization rules of the firefly and ant colony algorithm. For the graph, results after multi-level graph partitioning are transformed into a traveling salesman problem (TSP). This algorithm is used to optimize the load distribution of the solution, and finally, the rough graph segmentation is projected to obtain the most original segmentation optimization results. Although firefly algorithm (FA) and ant colony optimization (ACO), as swarm intelligence algorithms, are widely used to solve TSP problems, for the problems for which swarm intelligence algorithms easily fall into local optimization and low search accuracy, the improvement of the FaCO algorithm adjusts the weight of iterative location selection and updates the location. Experimental results on publicly available datasets such as the Oliver30 dataset and the eil51 dataset demonstrated the effectiveness of the FaCO algorithm. It is also significantly better than the commonly used firefly algorithm and other algorithms in terms of the search results and efficiency and achieves better results in optimizing the load-balancing problem of parallel computing.

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Moreover, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

LBMIC: communication-aware load balancing in distributed ASMs with evolving social networks

Multi-agent-based simulation for artificial stock market (ASM) is an important method in behavioural finance. The social network in ASM will influence the coordination and decision making of the intelligent agents. To improve the performance of an ASM with evolving social networks in a distributed computing environment, the computational load balancing and inter-nodes communication should be considered jointly. This paper proposes a scheduling algorithm called LBMIC to partition the agents onto different computing nodes while keeping the degree of load imbalance lower than a given threshold with minimized inter-nodes communication between agents. LBMIC models the scheduling into a graph partitioning problem and uses the multi-level graph partitioning algorithm to achieve an efficient scheduling. When the network evolves, LBMIC refines the partitioning by migrating parts of the agents. The experiments indicate that LBMIC can efficiently improve the performance of communication-intensive ASMs by both initial partitioning and refining partitioning.

Image segmentation using multilevel graph cuts and graph development using fuzzy rule‐based system

This research work deals with the segmentation of grey scale, colour and texture images using graph-based method. A graph is constructed using intensity, colour and texture profiles of image simultaneously. Based on nature of the image, a fuzzy rule-based system is used to find the weight that should be given to a specific image feature during the graph development. The fuzzy rule-based system provides a valuable approximation to cater the fact of imprecise knowledge (in our case knowledge about the involvement of a particular image feature in image). The graph is further used in multilevel graph-partitioning algorithm based on normalised graph cuts framework where it is iteratively bi-partitioned through normalised cuts to obtain optimum partitions. Multilevel algorithm makes the process fast enough to accommodate large databases as segmentation is often used in high-level image processing-techniques (i.e. object classification and recognition). Partitioned graph then results in segmented image. Berkeley segmentation database is used to experiment on the authors algorithm. The segmentation results are evaluated through probabilistic rand index and global consistency error methods. It is shown that the presented segmentation method provides effective results for most type of images.

Multilevel Segmentation of Histopathological Images Using Cooccurrence of Tissue Objects

This paper presents a new approach for unsupervised segmentation of histopathological tissue images. This approach has two main contributions. First, it introduces a new set of high-level texture features to represent the prior knowledge of spatial organization of the tissue components. These texture features are defined on the tissue components, which are approximately represented by tissue objects, and quantify the frequency of two component types being cooccurred in a particular spatial relationship. As they are defined on components, rather than on image pixels, these object cooccurrence features are expected to be less vulnerable to noise and variations that are typically observed at the pixel level of tissue images. Second, it proposes to obtain multiple segmentations by multilevel partitioning of a graph constructed on the tissue objects and combine them by an ensemble function. This multilevel graph partitioning algorithm introduces randomization in graph construction and refinements in its multilevel scheme to increase diversity of individual segmentations, and thus, improve the final result. The experiments on 200 colon tissue images reveal that the proposed approach--the object cooccurrence features together with the multilevel segmentation algorithm--is effective to obtain high-quality results. The experiments also show that it improves the segmentation results compared to the previous approaches.

Betweenness-based algorithm for a partition scale-free graph

Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that traditional partitioning algorithms are designed for random networks and regular networks, rather than for scale-free networks. Multilevel graph-partitioning algorithms are currently considered to be the state of the art and are used extensively. In this paper, we analyse the reasons why traditional multilevel graph-partitioning algorithms perform poorly and present a new multilevel graph-partitioning paradigm, top down partitioning, which derives its name from the comparison with the traditional bottom—up partitioning. A new multilevel partitioning algorithm, named betweenness-based partitioning algorithm, is also presented as an implementation of top—down partitioning paradigm. An experimental evaluation of seven different real-world scale-free networks shows that the betweenness-based partitioning algorithm significantly outperforms the existing state-of-the-art approaches.

Multi-level sequential circuit partitioning for test vector generation for low power test in VLSI

Sequential graph partitioning algorithms have been developed to fulfill the requirements of emerging multi-phase problems in circuit testing models. In this paper, we present a multi-level graph partitioning algorithm for circuit partitioning, which will minimize the number of test vectors during a low power test in VLSI circuits. By reducing the number of test vectors, we can reduce the energy consumption during the test. Our experimental results with ISCAS bench mark circuits have shown that the power can be reduced up to 55%.

Using graph partitioning to discover regions of correlated spatio-temporal change in evolving graphs

There is growing interest in studying dynamic graphs, or graphs that evolve with time. In this work, we investigate a new type of dynamic graph analysis - finding regions of a graph that are evolving in a similar manner and are topologically similar over a period of time. For example, these regions can be used to group a set of changes having a common cause in event detection and fault diagnosis. Prior work [6] has proposed a greedy framework called cSTAG to find these regions. It was accurate in datasets where the regions are temporally and spatially well separated. However, in cases where the regions are not well separated, cSTAG produces incorrect groupings. In this paper, we propose a new algorithm called regHunter. It treats the region discovery problem as a multi-objective optimisation problem, and it uses a multi-level graph partitioning algorithm to discover the regions of correlated change. In addition, we propose an external clustering validation technique, and use several existing internal measures to evaluate the accuracy of regHunter. Using synthetic datasets, we found regHunter is significantly more accurate than cSTAG in dynamic graphs that have regions with small separation. Using two real datasets - the access graph of the 1998 World Cup website, and the BGP connectivity graph during the landfall of Hurricane Katrina - we found regHunter obtained more accurate results than cSTAG. Furthermore, regHunter was able to discover two interesting regions for the World Cup access graph that CSTAG was not able to find.

Construction of a reference gene association network from multiple profiling data: application to data analysis

Gene expression profiling is an important tool for gaining insight into biology. Novel strategies are required to analyze the growing archives of microarray data and extract useful information from them. One area of interest is in the construction of gene association networks from collections of profiling data. Various approaches have been proposed to construct gene networks using profiling data, and these networks have been used in functional inference as well as in data visualization. Here, we investigated a non-parametric approach to translate profiling data into a gene network. We explored the characteristics and utility of the resulting network and investigated the use of network information in analysis of variance models and hypothesis testing. Our work is composed of two parts: gene network construction and partitioning and hypothesis testing using sub-networks as groups. In the first part, multiple independently collected microarray datasets from the Gene Expression Omnibus data repository were analyzed to identify probe pairs that are positively co-regulated across the samples. A co-expression network was constructed based on a reciprocal ranking criteria and a false discovery rate analysis. We named this network Reference Gene Association (RGA) network. Then, the network was partitioned into densely connected sub-networks of probes using a multilevel graph partitioning algorithm. In the second part, we proposed a new, MANOVA-based approach that can take individual probe expression values as input and perform hypothesis testing at the sub-network level. We applied this MANOVA methodology to two published studies and our analysis indicated that the methodology is both effective and sensitive for identifying transcriptional sub-networks or pathways that are perturbed across treatments.

Region-based hierarchical operation partitioning for multicluster processors

Clustered architectures are a solution to the bottleneck of centralized register files in superscalar and VLIW processors. The main challenge associated with clustered architectures is compiler support to effectively partition operations across the available resources on each cluster. In this work, we present a novel technique for clustering operations based on graph partitioning methods. Our approach incorporates new methods of assigning weights to nodes and edges within the dataflow graph to guide the partitioner. Nodes are assigned weights to reflect their resource usage within a cluster, while a slack distribution method intelligently assigns weights to edges to reflect the cost of inserting moves across clusters. A multilevel graph partitioning algorithm, which globally divides a dataflow graph into multiple parts in a hierarchical manner, uses these weights to efficiently generate estimates for the quality of partitions. We found that our algorithm was able to achieve an average of 20% improvement in DSP kernels and 5% improvement in SPECint2000 for a four-cluster architecture.

Automatic decomposition of unstructured meshes employing genetic algorithms for parallel FEM computations

Parallel execution of computational mechanics codes requires efficient mesh-partitioning techniques. These mesh-partitioning techniques divide the mesh into specified number of submeshes of approximately the same size and at the same time, minimise the interface nodes of the submeshes. This paper describes a new mesh partitioning technique, employing Genetic Algorithms. The proposed algorithm operates on the deduced graph (dual or nodal graph) of the given finite element mesh rather than directly on the mesh itself. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialise an optimisation of the graph partition problem. In practice, hierarchy of (usually more than two) graphs are used to obtain the final graph partition. The proposed partitioning algorithm is applied to graphs derived from unstructured finite element meshes describing practical engineering problems and also several example graphs related to finite element meshes given in the literature. The test results indicate that the proposed GA based graph partitioning algorithm generates high quality partitions and are superior to spectral and multilevel graph partitioning algorithms.

Parallelization domain oriented multilevel graph partitioner

In this paper we present a novel multilevel graph partitioning algorithm, KACE, which uses knowledge about the domain and employs several graph transformation techniques. Both functional and structural parallelism in the sequential code are explored to improve the quality of parallel tasks. Statistical information about communication times between nodes as a function of message size and/or other factors are used to have a better estimate of balancing factors, code replication, and synchronization penalties. This enables us to use a task cohesion algorithm to obtain a coarse version of the partitioned graph. Many of KACE's parameters are shown to have definite impact on the parallelized program code.