HGED: A Hybrid Search Algorithm for Efficient Parallel Graph Edit Distance Computation

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently, the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation, we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

Graph edit distance (GED) is a fundamental measure for graph similarity analysis in many real applications. GED computation has known to be NP-hard and many heuristic methods are proposed. GED has two inherent characteristics: multiple optimum node matchings and one-to-one node matching constraints. However, these two characteristics have not been well considered in the existing learning-based methods, which leads to suboptimal models. In this paper, we propose a novel GED-specific loss function that simultaneously encodes the two characteristics. First, we propose an optimal partial node matching-based regularizer to encode multiple optimum node matchings. Second, we propose a plane intersection-based regularizer to impose the one-to-one constraints for the encoded node matchings. We use the graph neural network on the association graph of the two input graphs to learn the cross-graph representation. Our experiments show that our method is 4.2x-103.8x more accurate than the state-of-the-art methods on real-world benchmark graphs.

Graph edit distance is an error tolerant matching technique emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning and data mining; it represents the minimum-cost sequence of basic edit operations to transform one graph into another by means of insertion, deletion and substitution of vertices and/or edges. A widely used method for exact graph edit distance computation is based on the A* algorithm. To overcome its high memory load while traversing the search tree for storing pending solutions to be explored, we propose a depth-first graph edit distance algorithm which requires less memory and searching time. An evaluation of all possible solutions is performed without explicitly enumerating them all. Candidates are discarded using an upper and lower bounds strategy. A solid experimental study is proposed; experiments on a publicly available database empirically demonstrated that our approach is better than the A* graph edit distance computation in terms of speed, accuracy and classification rate.

A novel hierarchical-based framework for upper bound computation of graph edit distance

The definition of efficient similarity or dissimilarity measures between graphs is a key problem in structural pattern recognition. This problem is nicely addressed by the graph edit distance, which constitutes one of the most flexible graph dissimilarity measure in this field. Unfortunately, the computation of an exact graph edit distance is known to be exponential in the number of nodes. In the early beginning of this decade, an efficient heuristic based on a bipartite assignment algorithm has been proposed to find efficiently a suboptimal solution. This heuristic based on an optimal matching of nodes' neighborhood provides a good approximation of the exact edit distance for graphs with a large number of different labels and a high density. Unfortunately, this heuristic works poorly on unlabeled graphs or graphs with a poor diversity of neighborhoods. In this work we propose to extend this heuristic by considering a mapping of bags of walks centered on each node of both graphs.

It is essential to identify similarity between graphs for various tasks in data mining, machine learning and pattern recognition. Graph edit distance (GED) is the most popular graph similarity measure thanks to its flexibility and versatility. In this paper, we study the problem of top-<i>k</i> graph similarity search, which finds <i>k</i> graphs most similar to a given query graph under the GED measure. We propose incremental GED computation algorithms that compute desired GED lower and upper bounds. Based on the algorithms, we develop novel search frameworks to address the top-<i>k</i> search problem. Our frameworks are also designed to use a state-of-the art indexing technique to speed up top-<i>k</i> search. By conducting extensive experiments on real datasets, we show that the proposed frameworks significantly improve the performance of top-<i>k</i> graph similarity search.

To meet the objective of minimizing the job execution time, parallel computing has to deal with a lot of issues which crop up while working with parallel code. These issues can result in bottleneck and restrict the behavior of parallel program in attaining an aforesaid speedup as suggested by Amdahl Gene. The most problematic issue that crops up is the distribution of workload in both the categories of parallel system viz. homogeneous and heterogeneous systems. This situation demands an effective load balancing strategy to be in place in order to ensure a uniform distribution of load across the board. The scheduling `m' jobs to `n' resources with the objective to optimize the QoS parameters while balancing the load has been proven to be NP-hard problem. Therefore, a heuristic approach can be used to design an effective load balancing strategy. In this paper, a centralized dynamic load balancing strategy using adaptive thresholds has been proposed for a parallel system consisting of multiprocessors. The scheduler continuously monitors the load on the system and takes corrective measures as the load changes. The threshold values considered are adaptive in nature and are readjusted to suite the changing load on the system. Therefore, the scheduler always ensures a uniform distribution of the load on the processing elements with dynamic load environment.

An efficient, scalable, parallel algorithm for treating material surface contacts in solid mechanics finite element programs has been implemented in a modular way for MIMD parallel computers. The serial contact detection algorithm that was developed previously for the transient dynamics finite element code PRONTO3D has been extended for use in parallel computation by devising a dynamic (adaptive) processor load balancing scheme. 1

Image categorization: Graph edit [formula omitted] direction histogram

Feng, X.; Wan, M., and Li, S., 2020. The design of marine remote sensing image fusion model based on dynamic load balancing strategy. In: Yang, Y.; Mi, C.; Zhao, L., and Lam, S. (eds.), Global Topics and New Trends in Coastal Research: Port, Coastal and Ocean Engineering. Journal of Coastal Research, Special Issue No. 103, pp. 943–946. Coconut Creek (Florida), ISSN 0749-0208.In this work, a model of marine remote sensing image fusion based on dynamic load balancing is proposed. The remote sensing image acquisition system based on Android intelligent device obtains the marine remote sensing image, and enhances and registers the image based on the fuzzy theory and template matching, respectively, to realize the image preprocessing. Based on the preprocessing results, considering the small number of objects in the marine remote sensing image, the target area is divided by the idea of quad tree structure. At the same time, the task allocation strategy of dynamic load balancing and the idea of parallel computing are used to propose the task allocation algorithm processing model of the cluster system for the fusion processing of the image in the target area, so as to achieve the fusion of marine remote sensing image. It can be known that the proposed model takes less time and has superior average gradient and clarity of image.

The paper presents a parallel algorithm for computation of solvent accessible surface area of a molecule according to the Lee and Richards's (1971) algorithm. The efficient parallelization of this process is crucial in dynamic simulations of protein molecules and protein folding studies. The solvent accessible surface area (ASA) problem exhibits inherent parallelism that is exploited in the design of a parallel program which is implemented on an Intel iPSC machine. The performance of the parallel algorithm is enhanced by a dynamic load balancing scheme. The authors report on experiments performed on a set of protein structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, we propose to use a dynamic load balancing scheme that utilizes fixed relay stations placed in a cellular geographical coverage area to improve the handover performance in cellular networks. To this end, we develop closed-form performance expressions and derive the handover dropping probability in terms of the main system parameters, such as the new call and handover arrival rates, the number of fixed and load-balancing channels per cell, the load balancing probability for new and handover calls, etc. Our results show that by employing a dynamic load balancing scheme, not only the new call blocking probability, but also the handover dropping probability can be improved substantially, without reserving any channels or assigning any priority to handover calls. In fact, employing dynamic load balancing without any guard channels outperforms a conventional system that employs the well-known guard channel method (GCM).

The application of parallel computers to reservoir simulation is studied with the aid of two recently introduced Multiple Instruction, Multiple Data (MIMD) computers. The problems posed by reservoir simulators are shown to be particularly well suited for such parallel computers* Fundamental parallel programming techniques using Fortran are presented for the Hetrogeneous Element Processor (HEP) produced by Denelcor and the iPSC Hypercube produced by Intel. These techniques are then applied to two of the most time consuming tasks in reservoir simulation: forming the matrix coefficients and producing a sparse matrix solution. The problem of parallel formation of sparse matrix coefficients is addressed for the single and multiphase cases using both black oil and compositional fluid models. Parallel sparse matrix solution is addressed by considering D4 ordered Gaussian elimination, and the multigrid, conjugate gradient, and Successive Over-Relaxation (SOR) methods. Three parallel algorithms based on SOR are developed to illustrate the possible diversity of parallel algorithms. The red-black and multicolored SOR methods which are often used on vector machines are shown to be easily adaptable to parallel MIMD machine. Matrix partitioning and a new method of iteration pipelining are also presented as parallel SOR methods. The various SOR algorithms, in parallel form, are mapped onto the HEP to illustrate the speedups currently possible on an MIMD machine. Projections are made on the future importance of these types of machines to reservoir simulation.

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance. In this study, we perform a three-dimensional dendrite growth phase-field simulation in which AMR is implemented via parallel computing using multiple graphics processing units (GPUs), which provide high parallel computation performance. In the parallel GPU computation, we apply dynamic load balancing to parallel computing to equalize the computational cost per GPU. The accuracy of an AMR refinement condition is confirmed through the single-GPU computations of columnar dendrite growth during the directional solidification of a binary alloy. Next, we evaluate the efficiency of dynamic load balancing by performing multiple-GPU parallel computations for three different directional solidification simulations using a moving frame algorithm. Finally, weak scaling tests are performed to confirm the parallel efficiency of the developed code.