A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graph-based techniques in the Pattern Recognition and Machine Vision field.

/pdf/thirty-years-of-graph-matching-in-pattern-recognition-58lvpdkcaj.pdf

Thirty years of graph matching in pattern recognition

http://cjluserv.iis.sinica.edu.tw/~josephcclin/paper/cographs.pdf

Complement reducible graphs

In array processors it is important to map problem modules onto processors such that modules that communicate with each other lie, as far as possible, on adjacent processors. This mapping problem is formulated in graph theoretic terms and shown to be equivalent, in its most general form, to the graph isomorphism problem. The problem is also very similar to the bandwidth reduction problem for sparse matrices and to the quadratic assignment problem.

On the Mapping Problem

Approximate graph edit distance computation by means of bipartite graph matching

Along with the blossom of open source projects comes the convenience for software plagiarism. A company, if less self-disciplined, may be tempted to plagiarize some open source projects for its own products. Although current plagiarism detection tools appear sufficient for academic use, they are nevertheless short for fighting against serious plagiarists. For example, disguises like statement reordering and code insertion can effectively confuse these tools. In this paper, we develop a new plagiarism detection tool, called GPLAG, which detects plagiarism by mining program dependence graphs (PDGs). A PDG is a graphic representation of the data and control dependencies within a procedure. Because PDGs are nearly invariant during plagiarism, GPLAG is more effective than state-of-the-art tools for plagiarism detection. In order to make GPLAG scalable to large programs, a statistical lossy filter is proposed to prune the plagiarism search space. Experiment study shows that GPLAG is both effective and efficient: It detects plagiarism that easily slips over existing tools, and it usually takes a few seconds to find (simulated) plagiarism in programs having thousands of lines of code.

/pdf/gplag-detection-of-software-plagiarism-by-program-dependence-4cms55onj4.pdf

GPLAG: detection of software plagiarism by program dependence graph analysis

The isomorphism problem for graphs G1 and G2 is to determine if there exists a one-to-one mapping of the vertices of G1 onto the vertices of G2 such that two vertices of G1 are adjacent if and only if their images in G2 are adjacent. In addition to determining the existence of such an isomorphism, it is useful to be able to produce an isomorphism-inducing mapping in the case where one exists.The isomorphism problem for triconnected planar graphs is particularly simple since a triconnected planar graph has a unique embedding on a sphere [6]. Weinberg [5] exploited this fact in developing an algorithm for testing isomorphism of triconnected planar graphs in O(|V|2) time where V is the set consisting of the vertices of both graphs. The result has been extended to arbitrary planar graphs and improved to O(|V|log|V|) steps by Hopcroft and Tarjan [2,3]. In this paper, the time bound for planar graph isomorphism is improved to O(|V|). In addition to determining the isomorphism of two planar graphs, the algorithm can be easily extended to partition a set of planar graphs into equivalence classes of isomorphic graphs in time linear in the total number of vertices in all graphs in the set. A random access model of computation (see Cook [1]) is assumed. Although the proposed algorithm has a linear asymptotic growth rate, at the present stage of development it appears to be inefficient on account of a rather large constant. This paper is intended only to establish the existence of a linear algorithm which subsequent work might make truly efficient.

J. K. Wong

Papers

Linear time algorithm for isomorphism of planar graphs (Preliminary Report)