Analysis of Average Shortest-Path Length of Scale-Free Network

Computing the average shortest-path length of a large scale-free network needs much memory space and computation time. Hence, parallel computing must be applied. In order to solve the load-balancing problem for coarse-grained parallelization, the relationship between the computing time of a single-source shortest-path length of node and the features of node is studied. We present a dynamic programming model using the average outdegree of neighboring nodes of different levels as the variable and the minimum time difference as the target. The coefficients are determined on time measurable networks. A native array and multimap representation of network are presented to reduce the memory consumption of the network such that large networks can still be loaded into the memory of each computing core. The simplified load-balancing model is applied on a network of tens of millions of nodes. Our experiment shows that this model can solve the load-imbalance problem of large scale-free network very well. Also, the characteristic of this model can meet the requirements of networks with ever-increasing complexity and scale.

[1]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[2]  Ma Liang.  A New Approximation Algorithm for Finding Shortest-path in Large Networks , 2008 .

[3]  Bin Wu,et al.  Distance Distribution and Average Shortest Path Length Estimation in Real-World Networks , 2010, ADMA.

[4]  Aristides Gionis,et al.  Fast shortest path distance estimation in large networks , 2009, CIKM.

[5]  David A. Bader,et al.  An Experimental Study of A Parallel Shortest Path Algorithm for Solving Large-Scale Graph Instances , 2007, ALENEX.

[6]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[7]  Kurt Mehlhorn,et al.  A Parallelization of Dijkstra's Shortest Path Algorithm , 1998, MFCS.

[8]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[9]  Adilson E. Motter,et al.  Networks in Motion , 2012, ArXiv.

[10]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[11]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

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

[13]  B. Bollobás.  The evolution of random graphs , 1984 .

[14]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[15]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[16]  Jesper Larsson Träff,et al.  A Simple Parallel Algorithm for the Single-Source Shortest Path Problem on Planar Digraphs , 1996, IRREGULAR.

[17]  Zhang Ning.  Analysis of China Education Network Structure , 2007 .

[18]  Gerhard Weikum,et al.  Fast and accurate estimation of shortest paths in large graphs , 2010, CIKM.

[19]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .