A fast method to exactly calculate the diameter of incremental disconnected graphs

The breadth of problems requiring graph analytics is growing rapidly. Diameter is one of the most important metrics of a graph. The diameter is important in both designing algorithms for graphs and understanding the nature and evolution of graphs. Besides, the real world graphs are always changing. So detecting diameter in both static and dynamic graphs is very important. We first present an algorithm to calculate the diameter of the static graphs. The main goal of this algorithm is to reduce the number of breadth-first searches required to determine diameter of the graph. In addition, another algorithm is presented for calculating the diameter of incremental graphs. This algorithm uses the proposed static algorithm in its body. Based on experimental results, our proposed algorithm can detect diameter of both static and incremental graphs faster than existing approaches. To the best of our knowledge, the second algorithm is the first one that is able to efficiently determine the diameter of disconnected graphs that will be connected over time by adding new vertices.

[1]  Jure Leskovec,et al.  {SNAP Datasets}: {Stanford} Large Network Dataset Collection , 2014 .

[2]  Vijaya Ramachandran,et al.  The diameter of sparse random graphs , 2007, Random Struct. Algorithms.

[3]  Abhishek Kumar,et al.  Ulysses: a robust, low-diameter, low-latency peer-to-peer network , 2004, Eur. Trans. Telecommun..

[4]  Roberto Grossi,et al.  On computing the diameter of real-world undirected graphs , 2013, Theor. Comput. Sci..

[5]  Hector Garcia-Molina,et al.  Peer-to-peer research at Stanford , 2003, SGMD.

[6]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[7]  Yasuhiro Fujiwara,et al.  Real-Time Diameter Monitoring for Time-Evolving Graphs , 2011, DASFAA.

[8]  Roberto Grossi,et al.  Finding the Diameter in Real-World Graphs - Experimentally Turning a Lower Bound into an Upper Bound , 2010, ESA.

[9]  Wilfred Ng,et al.  Blogel: A Block-Centric Framework for Distributed Computation on Real-World Graphs , 2014, Proc. VLDB Endow..

[10]  Liam Roditty,et al.  Fast approximation algorithms for the diameter and radius of sparse graphs , 2013, STOC '13.

[11]  Roberto Grossi,et al.  On Computing the Diameter of Real-World Directed (Weighted) Graphs , 2012, SEA.

[12]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[13]  Azer Bestavros,et al.  Small-world characteristics of Internet topologies and implications on multicast scaling , 2006, Comput. Networks.

[14]  Robert E. Tarjan,et al.  Better Approximation Algorithms for the Graph Diameter , 2014, SODA.

[15]  Aart J. C. Bik,et al.  Pregel: a system for large-scale graph processing , 2010, SIGMOD Conference.

[16]  Raphael Yuster,et al.  Computing the diameter polynomially faster than APSP , 2010, ArXiv.

[17]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[18]  Uri Zwick,et al.  Exact and Approximate Distances in Graphs - A Survey , 2001, ESA.

[19]  Hassan Naderi,et al.  ExPregel: a new computational model for large‐scale graph processing , 2015, Concurr. Comput. Pract. Exp..

[20]  Takuya Akiba,et al.  An Exact Algorithm for Diameters of Large Real Directed Graphs , 2015, SEA.

[21]  Walter A. Kosters,et al.  Determining the diameter of small world networks , 2011, CIKM '11.