Skip to main content

Efficient computation of distance labeling for decremental updates in large dynamic graphs


Since today’s real-world graphs, such as social network graphs, are evolving all the time, it is of great importance to perform graph computations and analysis in these dynamic graphs. Due to the fact that many applications such as social network link analysis with the existence of inactive users need to handle failed links or nodes, decremental computation and maintenance for graphs is considered a challenging problem. Shortest path computation is one of the most fundamental operations for managing and analyzing large graphs. A number of indexing methods have been proposed to answer distance queries in static graphs. Unfortunately, there is little work on answering such queries for dynamic graphs. In this paper, we focus on the problem of computing the shortest path distance in dynamic graphs, particularly on decremental updates (i.e., edge deletions). We propose maintenance algorithms based on distance labeling, which can handle decremental updates efficiently. By exploiting properties of distance labeling in original graphs, we are able to efficiently maintain distance labeling for new graphs. We experimentally evaluate our algorithms using eleven real-world large graphs and confirm the effectiveness and efficiency of our approach. More specifically, our method can speed up index re-computation by up to an order of magnitude compared with the state-of-the-art method, Pruned Landmark Labeling (PLL).

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6



  2. Note that, we use a BFS manner to identify P A(0) and P A(8) in Algorithm 1 as we will show later that all vertices in P A(0) will appear consecutively in Lemma 5.





  1. Abraham, I., Delling, D., Goldberg, A.V., Werneck, R.F.F.: Hierarchical hub labelings for shortest paths. In: Proceedings of the 20th Annual European Symposium on Algorithms (ESA 2012), pp 24–35. Ljubljana (2012)

  2. Akiba, T., Iwata, Y., Yoshida, Y.: Fast exact shortest-path distance queries on large networks by pruned landmark labeling, pp 349–360. New York (2013)

  3. Akiba, T., Iwata, Y., Yoshida, Y.: Dynamic and historical shortest-path distance queries on large evolving networks by pruned landmark labeling. In: Proceedings of the 23rd International World Wide Web Conference (WWW 2014), pp 237–248. Seoul (2014)

  4. Akiba, T., Sommer, C., Kawarabayashi, K.: Shortest-path queries for complex networks: Exploiting low tree-width outside the core. In: Proceedings of the 15th International Conference on Extending Database Technology, (EDBT 2012), pp 144–155. Berlin (2012)

  5. Bernstein, A.: Maintaining shortest paths under deletions in weighted directed graphs: [Extended Abstract]. In: Proceedings of the 45th annual ACM symposium on Theory of computing (STOC 2013), pp 725–734. Palo Alto (2013)

  6. Bramandia, R., Choi, B., Ng, W.K.: Incremental maintenance of 2-hop labeling of large graphs. IEEE Trans. Knowl. Data Eng. 22(5), 682–698 (2010)

    Article  Google Scholar 

  7. Chang, L., Yu, J.X., Qin, L., Cheng, H., Qiao, M.: The exact distance to destination in undirected world. VLDB J. 21(6), 869–888 (2012)

    Article  Google Scholar 

  8. Cheng, J., Ke, Y., Chu, S., Cheng, C.: Efficient processing of distance queries in large graphs: A vertex cover approach. In: Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pp 457–468. Scottsdale (2012)

  9. Cheng, J., Yu, J.X.: On-line exact shortest distance query processing. In: EDBT, pp 481–492 (2009)

  10. Ciortea, A., Boissier, O., Zimmermann, A., Florea, A.M.: Reconsidering the social Web of things: Position paper. In: Proceedings the 2013 ACM International Joint Conference on Pervasive and Ubiquitous Computing (UbiComp 2013) (Adjunct Publication), pp 1535–1544. Zurich (2013)

  11. Cohen, E., Halperin, E., Kaplan, H., Zwick, U.: Reachability and distance queries via 2-hop labels. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp 937–946. San Francisco (2002)

  12. Demetrescu, C., Italiano, G.F.: A new approach to dynamic all pairs shortest paths. J. ACM 51(6), 968–992 (2004)

    MathSciNet  Article  MATH  Google Scholar 

  13. Demetrescu, C., Italiano, G.F.: Experimental analysis of dynamic all pairs shortest path algorithms. ACM Trans. Algorithms 2(4), 578–601 (2006)

    MathSciNet  Article  MATH  Google Scholar 

  14. Espinosa, J.: Facebook’s Global Growth in Q4: 1.06B MAU, Mobile Surpasses Web.

  15. Farsani, H.K., Nematbakhsh, M.A., Lausen, G.: SRank: Shortest paths as distance between nodes of a graph with application to RDF clustering. J. Inf. Sci. 39 (2), 198–210 (2013)

    Article  Google Scholar 

  16. Fu, A.W.C., Wu, H., Cheng, J., Wong, R.C.W.: IS-LABEL: An independent-set based labeling scheme for point-to-point distance querying. Proc. VLDB Endowment 6(6), 457–468 (2013)

    Article  Google Scholar 

  17. Jin, R., Ruan, N., Xiang, Y., Lee, V.E.: A highway-centric labeling approach for answering distance queries on large sparse graphs, pp 445–456. Scottsdale (2012)

  18. K., P., Kumar, S.P., Damien, D.: Ranked answer graph construction for keyword queries on RDF graphs without distance neighbourhood restriction. In: Proceedings of the 20th International Conference on World Wide Web (WWW 2011, Companion Volume), pp 361–366. Hyderabad (2011)

  19. Qin, Y., Sheng, Q.Z., Zhang, W.E.: SIEF: Efficiently answering distance queries for failure prone graphs. In: Proceedings of the 18th International Conference on Extending Database Technology (EDBT 2015), pp 145–156. Brussels (2015)

  20. Schenkel, R., Theobald, A., Weikum, G.: Efficient creation and incremental maintenance of the HOPI index for complex XML document collections. In: Proceedings of the 21st International Conference on Data Engineering (ICDE 2005), pp 360–371. Tokyo (2005)

  21. Vassilvitskii, S., Brill, E.: Using web-graph distance for relevance feedback in Web search. In: Proceedings of the 29th Annual International Conference on Research and Development in Information Retrieval (SIGIR 2006), pp 147–153. Seattle (2006)

  22. Vieira, M.V., Fonseca, B.M., Damazio, R., Golgher, P.B., de Castro Reis, D., Ribeiro-Neto, B.A.: Efficient search ranking in social networks. In: Proceedings of the 16th ACM Conference on Information and Knowledge Management (CIKM 2007), pp 563–572. Lisbon (2007)

  23. Wehmuth, K., Ziviani, A.: DACCER: Distributed assessment of the closeness centrality ranking in complex networks. Comput. Netw. 57(13), 2536–2548 (2013)

    Article  Google Scholar 

  24. Wei, F.: TEDI: Efficient shortest path query answering on graphs. In: Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD 2010), pp 99–110. Indianapolis (2010)

  25. Yao, L., Sheng, Q.Z.: Exploiting latent relevance for relational learning of ubiquitous things. In: Proceedings of the 21st ACM International Conference on Information and Knowledge Management (CIKM 2012). Maui (2012)

  26. Zhu, A.D., Xiao, X., Wang, S., Lin, W.: Efficient single-source shortest path and distance queries on large graphs. In: Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2013), pp 998–1006. Chicago (2013)

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Yongrui Qin.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Qin, Y., Sheng, Q.Z., Falkner, N.J.G. et al. Efficient computation of distance labeling for decremental updates in large dynamic graphs. World Wide Web 20, 915–937 (2017).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Shortest path
  • Graph computation
  • Distance labeling
  • Dynamic graph