A genetic algorithm and its parallelization for graph matching with similarity measures

Graph matching and similarity measures of graphs have many applications to pattern recognition, machine vision in robotics, and similarity-based approximate reasoning in artificial intelligence. This paper proposes a method of matching and a similarity measure between two directed labeled graphs. We define the degree of similarity, the similar correspondence, and the similarity map which denotes the matching between the graphs. As an approximate computing method, we apply genetic algorithms (GA) to find a similarity map and compute the degree of similarity between graphs. For speed, we make parallel implementations in almost all steps of the GA. We have implemented the sequential GA and the parallel GA in C programs, and made simulations for both GAs. The simulation results show that our method is efficient and useful. This work was presented, in part, at the Second International Symposium on Artificial Life and Robotics, Oita Japan, February 18–20, 1997     

An adjustable linear time parallel algorithm for maximum weight bipartite matching

We present a parallel algorithm for finding a maximum weight matching in general bipartite graphs with an adjustable time complexity of using O(nmax(2ω,4+ω)) processing elements for ω?1. Parameter ω is not bounded. This is the fastest known strongly polynomial parallel algorithm to solve this problem. This is also the first adjustable parallel algorithm for the maximum weight bipartite matching problem in which the execution time can be reduced by an unbounded factor. We also present a general approach for finding efficient parallel algorithms for the maximum matching problem.     

Kronecker product graph matching

In this paper the Interpolator-based Kronecker product graph matching (IBKPGM) algorithm for performing attributed graph matching is presented. The IBKPGM algorithm is based on the Kronecker product graph matching (KPGM) formulation. This new formulation incorporates a general approach to a wide class of graph matching problems based on attributed graphs, allowing the structure of the graphs to be based on multiple sets of attributes. Salient features of the IBKPGM algorithm are that no assumption is made about the adjacency structure of the graphs to be matched, and that the explicit calculation of compatibility values between all vertices of the reference and input graphs as well as between all edges of the reference and input graphs are avoided.     

Efficient parallel algorithms for graph problems

We present an efficient technique for parallel manipulation of data structures that avoids memory access conflicts. That is, this technique works on the Exclusive Read/Exclusive Write (EREW) model of computation, which is the weakest shared memory, MIMD machine model. It is used in a new parallel radix sort algorithm that is optimal for keys whose values are over a small range. Using the radix sort and known results for parallel prefix on linked lists, we develop parallel algorithms that efficiently solve various computations on trees and unicycular graphs. Finally, we develop parallel algorithms for connected components, spanning trees, minimum spanning trees, and other graph problems. All of the graph algorithms achieve linear speedup for all but the sparsest graphs.Part of this work was done while the first author was at the University of Illinois, Urbana-Champaign, the second author was at Carnegie-Mellon University, and the third author was at the Hebrew University and the Courant Institute of Mathematical Sciences, New York University. A preliminary version of this work was presented at the 1986 International Conference on Parallel Processing.     

A sparse nonnegative matrix factorization technique for graph matching problems

Graph matching problem that incorporates pairwise constraints can be cast as an Integer Quadratic Programming (IQP). Since it is NP-hard, approximate methods are required. In this paper, a new approximate method based on nonnegative matrix factorization with sparse constraints is presented. Firstly, the graph matching is formulated as an optimization problem with nonnegative and sparse constraints, followed by an efficient algorithm to solve this constrained problem. Then, we show the strong relationship between the sparsity of the relaxation solution and its effectiveness for graph matching based on our model. A key benefit of our method is that the solution is sparse and thus can approximately impose the one-to-one mapping constraints in the optimization process naturally. Therefore, our method can approximate the original IQP problem more closely than other approximate methods. Extensive and comparative experimental results on both synthetic and real-world data demonstrate the effectiveness of our graph matching method.     

Multivariate image similarity in the compressed domain using statistical graph matching

We address the problem of image similarity in the compressed domain, using a multivariate statistical test for comparing color distributions. Our approach is based on the multivariate Wald-Wolfowitz test, a nonparametric test that assesses the commonality between two different sets of multivariate observations. Using some pre-selected feature attributes, the similarity measure provides a comprehensive estimate of the match between different images based on graph theory and the notion of minimal spanning tree (MST). Feature extraction is directly provided from the JPEG discrete cosine transform (DCT) domain, without involving full decompression or inverse DCT. Based on the zig-zag scheme, a novel selection technique is introduced that guarantees image's enhanced invariance to geometric transformations. To demonstrate the performance of the proposed method, the application on a diverse collection of images has been systematically studied in a query-by-example image retrieval task. Experimental results show that a powerful measure of similarity between compressed images can emerge from the statistical comparison of their pattern representations.     

Work-efficient BSR-based parallel algorithms for some fundamental problems in graph theory

This paper presents BSR-parallel algorithms for some problems in fundamental graph theory : transitive closure, connected components, spanning tree, bridges and articulation points of a graph and bipartite graph recognition. There already exist constant time algorithms to solve these problems on a mesh with reconfigurable bus system using O(N ⁴) processors. Here we show that these problems can be solved in constant time using only O(N ²) processors on the BSR model (N is the number of vertices of the graph G). Therefore, our algorithms are more work-efficient. These new results suggest that many other problems in graph theory can be solved in constant time using the BSR model.     

A novel edge-centric approach for graph edit similarity computation

Graph similarity is an important notion with many applications. Graph edit distance is one of the most flexible graph similarity measures available. The main problem with this measure is that in practice it can only be computed for small graphs due to its exponential time complexity. This paper addresses the high complexity of graph edit distance computations. Specifically, we present CSI_GED, a novel edge-centric approach for computing graph edit distance through common sub-structure isomorphisms enumeration. CSI_GED utilizes backtracking search combined with a number of heuristics to reduce memory requirements and quickly prune away a large portion of the mapping search space. Experiments show that CSI_GED is highly efficient for computing graph edit distance; it outperforms the state-of-the-art methods by over three orders of magnitude. It also shows that CSI_GED scales the computation gracefully to larger and distant graphs on which current methods fail to run. Moreover, we evaluated CSI_GED as a stand-alone graph edit similarity search query method. The experiments show that CSI_GED is effective and scalable, and outperforms the state-of-the-art indexing-based methods by over two orders of magnitude.     

Inexact graph matching for model-based recognition: Evaluation and comparison of optimization algorithms

A method for segmentation and recognition of image structures based on graph homomorphisms is presented in this paper. It is a model-based recognition method where the input image is over-segmented and the obtained regions are represented by an attributed relational graph (ARG). This graph is then matched against a model graph thus accomplishing the model-based recognition task. This type of problem calls for inexact graph matching through a homomorphism between the graphs since no bijective correspondence can be expected, because of the over-segmentation of the image with respect to the model. The search for the best homomorphism is carried out by optimizing an objective function based on similarities between object and relational attributes defined on the graphs. The following optimization procedures are compared and discussed: deterministic tree search, for which new algorithms are detailed, genetic algorithms and estimation of distribution algorithms. In order to assess the performance of these algorithms using real data, experimental results on supervised classification of facial features using face images from public databases are presented.     

基于Zhang-Shasha算法的存储过程相似性匹配

Zhang-Shasha算法在度量有序树的距离以及相似度应用中具有独特的优势.针对学习者存储过程作业自动评估的问题,提出了一种基于Zhang-Shasha算法的存储过程相似性匹配的解决方法,关键在于如何把存储过程块转换成算法要求的有序树形式.采用词法分析和语法分析把存储过程转换成语法树,再转换成有序二叉树.通过分析转换所得的二叉树属于RB型树,Zhang-Shasha-R算法在计算此类型树的距离和相似度时具有较高的效率.分析实验结果,该方法的准确率较高,且随着实验中题量的增加,评估的准确率逐步提高.     

Fast algorithms for some dominating induced matching problems

We describe O(n)$O(n)$ time algorithms for finding the minimum weighted dominating induced matching of chordal, dually chordal, biconvex, and claw-free graphs. For the first three classes, we prove tight O(n)$O(n)$ bounds on the maximum number of edges that a graph having a dominating induced matching may contain. By applying these bounds, and employing existing O(n+m)$O(n+m)$ time algorithms we show that they can be reduced to O(n)$O(n)$ time. For claw-free graphs, we describe a variation of the existing algorithm for solving the unweighted version of the problem, which decreases its complexity from O(n²)$O(n^2)$ to O(n)$O(n)$, while additionally solving the weighted version. The same algorithm can be easily modified to count the number of DIM's of the given graph.     

Efficient parallel term matching and anti-unification

In this paper we present optimal processor x time parallel algorithms for term matching and anti-unification of terms represented as trees. Term matching is the special case of unification in which one of the terms is restricted to contain no variables. It has wide applicability to logic programming, term rewriting systems and symbolic pattern matching. Anti-unification is the dual problem of unification in which one computes the most specific generalization of two terms. It has application to inductive inference and theorem proving. Our algorithms run in O(log² N) time using N/log² N processors on a shared-memory model of computation that prohibits simultaneous reads or writes (EREW PRAM). These algorithms are the first polylogarithmic-time EREW algorithms with a processor x time product of the same order as that of their sequential counterparts, thereby permitting optimal speed-ups using any number of processors up to N/log² N. We also use the techniques developed in the paper to provide an N/log N-processor, O(log N)-time algorithm for a shared-memory model that allows both simultaneous reads and simultaneous writes (CRCW PRAM).Supported by NSF Grant IRI-88-09324 and NSF/DARPA Grant CCR-8908092.     

Fully dynamic algorithms for permutation graph coloring

We introduce a dynamic model for maintaining permutation graph coloring. Our motivation comes from the strait type river routing problem in VLSI. This paper presents fully dynamic algorithms for the permutation graph coloring problem. These algorithms are designed to handle Insert and Delete operations and answer some queries. The aim is to provide for running times that are asymptotically more efficient than recomputation (off-line algorithms that run in 0(n logw) time, are known [5,6,10,3]). First, the algorithm A^ that runs in 0(n) uniform running time per Insert/Delete operation is presented. Second, a more sophisticated data structure leads to the algorithm A2 that runs in (9(m logw) uniform running time per Insert I Delete, where m denotes the number of chains in the decomposition. It follows from [7,4] that the running time of A2 when the points from the dynamically changing set are drawn independently from a uniform distribution on the unit square is G(yfn logn) per Insert/Delete in probability. Third, we sketch a composite algorithm A3 that switches between A± and A2 guarantees an amortized running time of (min{n,m logw)) per Insert/Delete. Finally, we outline a number of applications     

Marking student programs using graph similarity

We present a novel approach to the automated marking of student programming assignments. Our technique quantifies the structural similarity between unmarked student submissions and marked solutions, and is the basis by which we assign marks. This is accomplished through an efficient novel graph similarity measure (AssignSim). Our experiments show good correlation of assigned marks with that of a human marker.     

Orderly algorithms for graph generation

The existence of orderly analogues of graph generators proposed by Heap and Farrell is established. The modifications to these algorithms supply practical methods enabling one to generate exhaustive lists of graphs and locally restricted graphs; moreover, the difficulty involved in ensuring that no duplications occur in the list is greatly reduced.     

Cellular matrix model for parallel combinatorial optimization algorithms in Euclidean plane

We propose a parallel computation model, called cellular matrix model (CMM), to address large-size Euclidean graph matching problems in the plane. The parallel computation takes place by partitioning the plane into a regular grid of cells, each cell being affected to a single processor. Each processor operates on local data, starting from its cell location and extending its search to the neighborhood cells in a spiral search way. In order to deal with large-size problems, memory size and processor number are fixed as O(N), where N is the problem size. Then one key point is that closest point searching in the plane is performed in O(1) expected time for uniform or bounded distribution, for each processor independently. We define a generic loop that models the parallel projection between graphs and their matching, as executed by the many cells at a given level of computation granularity. To illustrate its efficacy and versatility, we apply the CMM, on GPU platforms, to two problems in image processing: superpixel segmentation and stereo matching energy minimization. Firstly, we propose an extended version of the well-known SLIC superpixel segmentation algorithm, which we call SPASM algorithm, by using a parallel 2D self-organizing map instead of k-means algorithm. Secondly, we investigate the idea of distributed variable neighborhood search, and propose a parallel search heuristic, called distributed local search (DLS), for global energy minimization of stereo matching problem. We evaluate the approach with regards to the state-of-the-art graph cut and belief propagation algorithms. For each problem, we argue that the parallel GPU implementation provides new competitive quality/time trade-offs, with substantial acceleration factors as the problem size increases.     

几种图像相似性度量的匹配性能比较

针对景象匹配中匹配性能和匹配实时性会受相似性度量选择影响的问题,从常用的相似性度量（归一化积相关、相位相关、均平方差和去均值均平方差）入手,对图像施加噪声和进行畸变（如图像旋转变化、图像比例变化、光照强度变化和云层遮挡等）,通过相似性度量匹配性能的仿真试验,从匹配性、适应度和实时性等方面对各相似性度量进行比较,并对结果进行了归纳总结与证明。     

Fast exact string matching algorithms

String matching is the problem of finding all the occurrences of a pattern in a text. We propose a very fast new family of string matching algorithms based on hashing q-grams. The new algorithms are the fastest on many cases, in particular, on small size alphabets.     

结合匹配度和语义相似度的Deep Web查询接口模式匹配

查询接口模式匹配是Deep Web信息集成中的关键部分,双重相关性挖掘方法（DCM）能有效利用关联挖掘方法解决复杂接口模式匹配问题。针对DCM方法在匹配效率、匹配准确性方面的不足,提出了一种基于匹配度和语义相似度的新模式匹配方法。该方法首先使用矩阵存储属性间的关联关系,然后采用匹配度计算属性间的相关度,最后利用语义相似度计算候选匹配的相似性。通过在美国伊利诺斯大学的BAMM数据集上进行实验,所提方法与DCM及其改进方法比较有更高的匹配效率和准确性,表明该方法能更好地处理接口之间模式匹配问题。