Abstract
This paper presents a parallel version of the Maximal Clique Enumeration (MCE) approach for discovering tolerance classes. Finding such classes is a computationally complex problem, especially in the case of large data sets or in content-based retrieval applications(CBIR). The GPU implementation is an extension of earlier work by the authors on finding efficient methods for computing tolerance classes in images. The experimental results demonstrate that the GPU-based MCE algorithm is faster than the serial MCE implementation and can perform computations with higher values of tolerance ε.
This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grants 194376, 418413 and 185986. Tariq Alusaifeer has been supported by Government of Saudi Arabia.The authors wish to thank Prof. J. Wang for sharing the SIMPlicity image database.
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References
Akkoyunlu, E.A.: The enumeration of maximal cliques of large graphs. SIAM Journal on Computing 2(1), 1–6 (1973)
Bomze, I., Budinich, M., Pardalos, P., Pelillo, M.: The maximum clique problem. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, vol. 4. Kluwer (1999)
Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Communications of the ACM 16(9), 575–577 (1973)
Cazals, F., Karande, C.: A note on the problem of reporting maximal cliques. Theoretical Computer Science 407(1), 564–568 (2008)
Harary, F., Ross, I.C.: A procedure for clique detection using the group matrix. Sociometry 20(3), 205–215 (1957)
Henry, C.J.: Near Sets: Theory and Applications. Ph.D. thesis (2010)
Henry, C.J.: Perceptual indiscernibility, rough sets, descriptively near sets, and image analysis. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XV. LNCS, vol. 7255, pp. 41–121. Springer, Heidelberg (2012)
Henry, C.J., Ramanna, S.: Signature-based perceptual nearness. Application of near sets to image retrieval. Mathematics in Computer Science, 71–85
Henry, C.J., Ramanna, S.: Parallel computation in finding near neighbourhoods. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 523–532. Springer, Heidelberg (2011)
Henry, C.J., Ramanna, S.: Maximal clique enumeration in finding near neighbourhoods. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds.) Transactions on Rough Sets XVI. LNCS, vol. 7736, pp. 103–124. Springer, Heidelberg (2013)
Henry, C.J., Ramanna, S., Levi, D.: Qantifying nearness in visual spaces. Cybernetics and Systems 44(1), 38–56 (2013)
Jenkins, J., Arkatkar, I., Owens, J.D., Choudhary, A., Samatova, N.F.: Lessons learned from exploring the backtracking paradigm on the GPU. In: Proceedings of the 17th International Conference on Parallel Processing, vol. II, pp. 425–437 (2011)
Kirk, D.B., Hwu, W.W.: Programming Massively Parallel Processors: A Hands-on Approach. Morgan Kaufmann, Waltham (2013)
Koch, I.: Fundamental study: Enumerating all connected maximal common sugraphs in two graphs. Theoretical Computer Science 250(1-2), 1–30 (2001)
Li, J., Wang, J.Z.: Automatic linguistic indexing of pictures by a statistical modeling approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(9), 1075–1088 (2003)
Makino, K., Uno, T.: New algorithms for enumerating all maximal cliques. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 260–272. Springer, Heidelberg (2004)
Peters, J.F.: Near sets. General theory about nearness of objects. Applied Mathematical Sciences 1(53), 2609–2629 (2007)
Peters, J.F.: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 1(4), 239–245 (2009)
Peters, J.F.: Corrigenda and addenda: Tolerance near sets and image correspondence. International Journal of Bio-Inspired Computation 2(5), 310–318 (2010)
Peters, J.F., Naimpally, S.: Applications of near sets. Amer. Math. Soc. Notices 59(4), 536–542 (2012)
Peters, J.F., Wasilewski, P.: Foundations of near sets. Information Sciences 179(18), 3091–3109 (2009)
Peters, J.F., Wasilewski, P.: Tolerance spaces: Origins, theoretical aspects and applications. Information Sciences 195, 211–225 (2012)
Rubner, Y., Tomasi, C., Guibas, L.J.: A metric for distributions with applications to image databases. In: Proceedings of the 1998 IEEE International Conference on Computer Vision, pp. 59–66 (1998)
Schmidt, M.C., Samatova, N.F., Thomas, K., Byung-Hoon, P.: A scalable, parallel algorithm for maximal clique enumeration. Journal of Parallel and Distributed Computing 69, 417–428 (2009)
Smeulders, A.W.M., Worring, M., Santini, S., Gupta, A., Jain, R.: Content-based image retrieval at the end of the early years. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(12), 1349–1380 (2000)
Sossinsky, A.B.: Tolerance space theory and some applications. Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications 5(2), 137–167 (1986)
Tsukiyama, S., Ide, M., Ariyoshi, H., Shirakawa, I.: A new algorithm for generating all the maximal independent sets. SIAM Journal on Computing 6, 505–517 (1977)
Wang, J.Z., Li, J., Wiederhold, G.: SIMPLIcity: Semantics-sensitive integrated matching for picture libraries. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(9), 947–963 (2001)
Wolski, M.: Granular computing: Topological and categorical aspects of near and rough set approaches to granulation of knowledge. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds.) Transactions on Rough Sets XVI. LNCS, vol. 7736, pp. 34–52. Springer, Heidelberg (2013)
Zeeman, E.C.: The topology of the brain and the visual perception, pp. 240–256. Prentice Hall, New Jersey (1965)
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Alusaifeer, T., Ramanna, S., Henry, C.J., Peters, J. (2013). GPU Implementation of MCE Approach to Finding Near Neighbourhoods. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds) Rough Sets and Knowledge Technology. RSKT 2013. Lecture Notes in Computer Science(), vol 8171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41299-8_24
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DOI: https://doi.org/10.1007/978-3-642-41299-8_24
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