Algoritmo de reducción de grafos sin pérdida de información
Graph Reduction Algorithm without Loss of Information
Rafael Rodríguez-Puente y Manuel S. Lazo-Cortés
Universidad de las Ciencias Informáticas, La Habana, Cuba. rafaelrp@uci.cu, manuellazo55@gmail.com
]]>Resumen
Los algoritmos relacionados con la teoría de grafos han sido ampliamente estudiados. Varios estudios se enfocan en la disminución de la complejidad temporal de estos algoritmos. Las técnicas utilizadas en este sentido, generalmente se basan en reducir un grafo o el espacio de búsqueda de solución, eliminando información redundante para el problema específico que se desea resolver. El proceso de reducción de un grafo consiste en obtener grafos más pequeños (con menos vértices) que tengan las características principales o relevantes del grafo original. En el caso de la búsqueda de caminos óptimos, los algoritmos que hacen uso de la reducción de grafos o del espacio de búsqueda de solución, no garantizan la obtención del óptimo en todos los casos. Lo mismo ocurre en otros tipos de problemas tales como la reducción de grafos en redes de workflow, de computadoras, etc. En este trabajo se propone un algoritmo de reducción de grafos sin pérdida de información. La propuesta tiene una forma flexible de especificar la manera en que se quiere reducir el grafo; por consiguiente, puede ser utilizada en la solución de varios tipos de problemas, contribuyendo a la obtención de respuestas óptimas en tiempos menores.
Palabras clave. Reducción de grafos, reescritura de grafos, búsqueda de caminos óptimos.
Abstract.
Algorithms related to graph theory have been studied widely. Several studies deal with the reduction of temporal complexity of these algorithms. The techniques used in this sense are generally based on reducing the graph or the search space of solution. These approaches remove redundant information for a specific kind of problem. The process of reducing a graph is based on obtaining smaller graphs (with fewer vertices) with major or relevant characteristics of the original graph. Algorithms that make use of the graph reduction approach (or reduction of solution search space) for the shortest path search do not guarantee obtaining an optimal path in all cases. The same applies to other types of problems such as graph reduction in workflow networks, computer networks, etc. In this paper we propose a graph reduction algorithm without loss of information. Our method is characterized by a flexible way to specify in what manner in it desirable to reduce a given graph. Therefore, our proposal can be used in solving various types of problems and obtaining optimal responses in less time.
Keywords. Graph reduction, graph rewriting, shortest path search.
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1. Bast, H., Funke, S., Sanders, P., & Schultes, D. (2007). Fast Routing in Road Networks with Transit Nodes. Science, 316(5824), 566-566. [ Links ]
2. Casetti, C., Lo Cigno, R., Mellia, M., Munafo, M., & Zsóka, Z. (2003). A new class of QoS routing strategies based on network graph reduction. Computer Networks, 41(4), 475-487. [ Links ]
3. Cong, J., Fang, J., & Khoo, K.Y. (1999). An implicit connection graph maze routing algorithm for ECO routing. 1999 IEEE/ACM International Conference on Computer-Aided Design, San Jose, CA, USA, 163-167. [ Links ]
4. Dijkstra, E.W. (1959). A Note on Two Problems in Connexion with Graphs. Numerische Mathematik, 1(1), 269-271. [ Links ]
]]>5. Geisberger, R., Sanders, P., Schultes, D., & Delling, D. (2008). Contraction hierarchies: Faster and simpler hierarchical routing in road networks. 7th International Conference on Experimental Algorithms (WEA'08), Massachusetts, USA, 319-333. [ Links ]
6. Gonzalez, H., Han, J., Li, X., Myslinska, M., & Sondag, J.P. (2007). Adaptive fastest path computation on a road network: a traffic mining approach. 33rd International Conference on Very Large Data Bases (VLDB'07), Vienna, Austria, 794-805. [ Links ]
7. Gutman, R.J. (2004). Reach-Based Routing: A New Approach to Shortest Path Algorithms Optimized for Road Networks. Proceedings of the Sixth Workshop on Algorithm Engineering and Experiments and the First Workshop on Analytic Algorithmics and Combinatorics, New Orleans, LA, USA, 100-111. [ Links ]
8. Hoare, C.A.R. (1969). An axiomatic basis for computer programming. Communications of the ACM, 12(10), 576-580. [ Links ]
9. Janssens, D. & Rozenberg, G. (1982). Graph grammars with neighbourhood-controlled embedding. Theoretical Computer Science, 21(1), 55-74. [ Links ]
]]>10. Li, Y.L., Li, J.Y., & Chen, W.B. (2007). An efficient tile-based ECO router using routing graph reduction and enhanced global routing flow. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 26(2), 345-358. [ Links ]
11. Lin, H., Zhao, Z., Li, H., & Chen, Z. (2002). A novel graph reduction algorithm to identify structural conflicts. 35th Annual Hawaii International Conference on System Sciences, Big Island, Hawaii, 1-10. [ Links ]
12. Liu, Q., Cao, B., & Zhao, Y. (2010). An improved verification method for workflow model based on Petri net reduction. 2nd IEEE International Conference on Information Management and Engineering (ICIME), Chengdu, China, 252-256. [ Links ]
13. Lu, K. & Liu, Q. (2007). An algorithm combining graph-reduction and graph-search for workflow graphs verification. 11th International Conference on Computer Supported Cooperative Work in Design, Melbourne, Australia, 772-776. [ Links ]
14. Pfoser, D., Efentakis, A., Voisard, A., & Wenk, C. (2009). Exploiting road network properties in efficient shortest path computation (TR-09-007). Berkeley, CA, USA: International Computer Science Institute. [ Links ]
]]>15. Rodríguez-Puente, R. & Lazo-Cortés, M.S. (2013). Algorithm for shortest path search in Geographic Information Systems by using reduced graphs. SpringerPlus, 2, Art. No.291. [ Links ]
16. Rodríguez-Puente, R., Marrero-Osorio, S.A., & Lazo-Cortés, M.S. (2012). Aplicación de un algoritmo de reducción de grafos al Método de los Grafos Dicromáticos. Ingeniería Mecánica, 15(2),158-169. [ Links ]
17. Sadiq, W. & Orlowska, M.E. (2000). Analyzing process models using graph reduction techniques. Information systems, 25(2), 117-134. [ Links ]
18. Sanders, P. & Schultes, D. (2005). Highway hierarchies hasten exact shortest path queries. Algorithms-Esa 2005, Lecture Notes in Computer Science, 568-579. [ Links ]
19. Xing, Z. & Kao, R. (2002). Shortest path search using tiles and piecewise linear cost propagation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 21(2), 145-158. [ Links ]
]]>20. Zheng, S.Q., Lim, J.S., & Iyengar, S.S. (1996). Finding obstacle-avoiding shortest paths using implicit connection graphs. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 15(1), 103-110. [ Links ]
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