Parallel algorithms for tensor product-based inexact graph matching

In this paper we face the inexact graph matching problem from the parallel algorithms viewpoint. After a brief introduction of both graph matching and parallel computing contexts, we discuss a specific method of performing inexact graph matching based on the well known tensor product operator. We analyze the problem using two parallel computing models, following different algorithmic strategies, and performing also an experimental evaluation. The aim of this paper is to provide modeling and algorithmic strategies to extend inexact graph matching methods to graphs of high order and size, conceiving the computational problem in the more wider context of graph-based Pattern Recognition and Soft Computing systems. As a whole, the obtained results encourage more effort on this direction.

[1]  Dong Hoon Lee,et al.  Secure Similarity Search , 2007 .

[2]  Allan Borodin,et al.  On Relating Time and Space to Size and Depth , 1977, SIAM J. Comput..

[3]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[4]  S. V. N. Vishwanathan,et al.  Graph kernels , 2007 .

[5]  Kaspar Riesen,et al.  Graph Classification and Clustering Based on Vector Space Embedding , 2010, Series in Machine Perception and Artificial Intelligence.

[6]  H. James Hoover,et al.  Limits to Parallel Computation: P-Completeness Theory , 1995 .

[7]  Thomas Gärtner,et al.  Why Kernels for Structured Data , 2008 .

[8]  Kaspar Riesen,et al.  Approximate graph edit distance computation by means of bipartite graph matching , 2009, Image Vis. Comput..

[9]  Clyde P. Kruskal,et al.  Submachine Locality in the Bulk Synchronous Setting (Extended Abstract) , 1996, Euro-Par, Vol. II.

[10]  J. Pach,et al.  Wiley‐Interscience Series in Discrete Mathematics and Optimization , 2011 .

[11]  Antonello Rizzi,et al.  Automatic Classification of Graphs by Symbolic Histograms , 2007, 2007 IEEE International Conference on Granular Computing (GRC 2007).

[12]  Jens H. Krüger,et al.  A Survey of General‐Purpose Computation on Graphics Hardware , 2007, Eurographics.

[13]  Geppino Pucci,et al.  On the Effectiveness of D-BSP as a Bridging Model of Parallel Computation , 2001, International Conference on Computational Science.

[14]  Lorenzo Livi,et al.  Graph Recognition by Seriation and Frequent Substructures Mining , 2012, ICPRAM.

[15]  Antonello Rizzi,et al.  Neurofuzzy Min-Max Networks Implementation on FPGA , 2011, IJCCI.

[16]  Leslie G. Valiant,et al.  A bridging model for parallel computation , 1990, CACM.

[17]  Lorenzo Livi,et al.  Inexact Graph Matching through Graph Coverage , 2012, ICPRAM.

[18]  Horst Bunke,et al.  A Random Walk Kernel Derived from Graph Edit Distance , 2006, SSPR/SPR.

[19]  Steven Fortune,et al.  Parallelism in random access machines , 1978, STOC.

[20]  Sanguthevar Rajasekaran,et al.  Handbook of Parallel Computing - Models, Algorithms and Applications , 2007 .

[21]  W. Imrich,et al.  Product Graphs: Structure and Recognition , 2000 .

[22]  Jie Cheng,et al.  Programming Massively Parallel Processors. A Hands-on Approach , 2010, Scalable Comput. Pract. Exp..

[23]  Leslie M. Goldschlager,et al.  A universal interconnection pattern for parallel computers , 1982, JACM.

[24]  James Demmel,et al.  Benchmarking GPUs to tune dense linear algebra , 2008, 2008 SC - International Conference for High Performance Computing, Networking, Storage and Analysis.

[25]  E. Sampathkumar.  On tensor product graphs , 1975 .

[26]  Kun Zhou,et al.  BSGP: bulk-synchronous GPU programming , 2008, ACM Trans. Graph..

[27]  Kaspar Riesen,et al.  Fast Suboptimal Algorithms for the Computation of Graph Edit Distance , 2006, SSPR/SPR.

[28]  Leslie G. Valiant,et al.  A bridging model for multi-core computing , 2008, J. Comput. Syst. Sci..

[29]  Hans-Peter Kriegel,et al.  Protein function prediction via graph kernels , 2005, ISMB.