A critical examination of node-similarity based graph matching algorithms

In this paper, we shall critically examine a special class of graph matching algorithms that follow the approach of node-similarity measurement. A high-level algorithm framework, namely node-similarity graph matching framework (NSGM framework), is proposed, from which, many existing graph matching algorithms can be subsumed, including the eigen-decomposition method of Umeyama, the polynomial-transformation method of Almohamad, the hubs and authorities method of Kleinberg, and the kronecker product successive projection methods of Wyk, etc. In addition, improved algorithms can be developed from the NSGM framework with respects to the corresponding results in graph theory. As the observation, it is pointed out that, in general, any algorithm which can be subsumed from NSGM framework fails to work well for graphs with non-trivial auto-isomorphism structure.

Measuring similarity of software designs using graph matching for CBR

This paper examines different ways of measuring similarity between software design models for Case Based Reasoning (CBR) to facilitate reuse of software design and code. The paper considers structural and behavioural aspects of similarity between software design models. Similarity metrics for comparing static class structures are defined and discussed. A Graph representation of UML class diagrams and corresponding similarity measures for UML class diagrams are defined. A full search graph matching algorithm for measuring structural similarity diagrams based on the identification of the Maximum Common Sub-graph (MCS) is presented. Finally, a simple evaluation of the approach is presented and discussed.

Matching case history patterns in case-based reasoning

This paper introduces a mechanism for representing and recognizing case history patterns with rich internal temporal aspects. A case history is characterized as a collection of elemental cases as in conventional case-based reasoning systems, together with the corresponding temporal constraints that can be relative and/or with absolute values. A graphical representation for case histories is proposed as a directed, partially weighted and labeled simple graph. In terms of such a graphical representation, an eigen-decomposition graph matching algorithm is proposed for recognizing case history patterns.

A robust approach to subsequence matching

In terms of a general time theory which addresses time-elements as typed point-based intervals, a formal characterization of time-series and state-sequences is introduced. Based on this framework, the subsequence matching problem is specially tackled by means of being transferred into bipartite graph matching problem. Then a hybrid similarity model with high tolerance of inversion, crossover and noise is proposed for matching the corresponding bipartite graphs involving both temporal and non-temporal measurements. Experimental results on reconstructed time-series data from UCI KDD Archive demonstrate that such an approach is more effective comparing with the traditional similarity model based algorithms, promising robust techniques for lager time-series databases and real-life applications such as Content-based Video Retrieval (CBVR), etc.

Maintenance of a case-base for the retrieval of rotationally symmetric shapes for the design of metal castings

In this paper, we discuss the problem of maintenance of a CBR system for retrieval of rotationally symmetric shapes. The special feature of this system is that similarity is derived primarily from graph matching algorithms. The special problem of such a system is that it does not operate on search indices that may be derived from single cases and then used for visualisation and principle component analyses. Rather, the system is built on a similarity metric defined directly over pairs of cases. The problems of efficiency, consistency, redundancy, completeness and correctness are discussed for such a system. Performance measures for the CBR system are given, and the results for trials of the system are presented. The competence of the current case-base is discussed, with reference to a representation of cases as points in an n-dimensional feature space, and a Gramian visualisation. A refinement of the case base is performed as a result of the competence analysis and the performance of the case-base before and after refinement is compared.

Representing and recognizing scenario patterns

This paper presents a formal method for representing and recognizing scenario patterns with rich internal temporal aspects. A scenario is presented as a collection of time-independent fluents, together with the corresponding temporal knowledge that can be relative and/or with absolute values. A graphical representation for temporal scenarios is introduced which supports consistence checking as for the temporal constraints. In terms of such a graphical representation, graph-matching algorithms/methodologies can be directly adopted for recognizing scenario patterns.

Applying CBR to measure similarity of software design structures

This paper examines different ways for measuring similarity between software design models for the purpose of software reuse. Current approaches to this problem are discussed and a set of suitable similarity metrics are proposed and evaluated. Work on the optimisation of weights to increase the competence of a CBR system is presented. A graph matching algorithm and associated metrics capturing the structural similarity between UML class diagrams is presented and demonstrated through an example case.

Parallel dynamic graph-partitioning for unstructured meshes

A parallel method for the dynamic partitioning of unstructured meshes is described. The method introduces a new iterative optimization technique known as relative gain optimization which both balances the workload and attempts to minimize the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.

A multilevel algorithm for force-directed graph drawing

We describe a heuristic method for drawing graphs which uses a multilevel technique combined with a force-directed placement algorithm. The multilevel process groups vertices to form clusters, uses the clusters to define a new graph and is repeated until the graph size falls below some threshold. The coarsest graph is then given an initial layout and the layout is successively refined on all the graphs starting with the coarsest and ending with the original. In this way the multilevel algorithm both accelerates and gives a more global quality to the force- directed placement. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on a number of examples ranging from 500 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 30 seconds for a 10,000 vertex graph to around 10 minutes for the largest graph. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

A framework for historical case-based reasoning

This paper presents a framework for Historical Case-Based Reasoning (HCBR) which allows the expression of both relative and absolute temporal knowledge, representing case histories in the real world. The formalism is founded on a general temporal theory that accommodates both points and intervals as primitive time elements. A case history is formally defined as a collection of (time-independent) elemental cases, together with its corresponding temporal reference. Case history matching is two-fold, i.e., there are two similarity values need to be computed: the non-temporal similarity degree and the temporal similarity degree. On the one hand, based on elemental case matching, the non-temporal similarity degree between case histories is defined by means of computing the unions and intersections of the involved elemental cases. On the other hand, by means of the graphical presentation of temporal references, the temporal similarity degree in case history matching is transformed into conventional graph similarity measurement.

A multilevel algorithm for force-directed graph-drawing

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm. The multilevel technique matches and coalesces pairs of adjacent vertices to define a new graph and is repeated recursively to create a hierarchy of increasingly coarse graphs, G0, G1, …, GL. The coarsest graph, GL, is then given an initial layout and the layout is refined and extended to all the graphs starting with the coarsest and ending with the original. At each successive change of level, l, the initial layout for Gl is taken from its coarser and smaller child graph, Gl+1, and refined using force-directed placement. In this way the multilevel framework both accelerates and appears to give a more global quality to the drawing. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on examples ranging in size from 10 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 12 seconds for a 10,000 vertex graph to around 5-7 minutes for the largest graphs. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

A combined evolutionary search and multilevel optimisation approach to graph-partitioning

The graph-partitioning problem is to divide a graph into several pieces so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges is minimised. Important applications of the problem arise, for example, in parallel processing where data sets need to be distributed across the memory of a parallel machine. Very effective heuristic algorithms have been developed for this problem which run in real-time, but it is not known how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. A distinctive feature is the use of a multilevel heuristic algorithm to provide an effective crossover. The technique is tested on several example graphs and it is demonstrated that our method can achieve extremely high quality partitions significantly better than those found by the state-of-the-art graph-partitioning packages.