Total Positive Influence Domination on Weighted Networks

We are proposing two greedy and a new linear programming based approximation algorithm for the total positive influence dominating set problem in weighted networks. Applications of this problem in weighted settings include finding: a minimum cost set of nodes to broadcast a message in social networks, such that each node has majority of neighbours broadcasting that message; a maximum trusted set in bitcoin network; an optimal set of hosts when running distributed apps etc.. Extensive experiments on different generated and real networks highlight advantages and potential issues for each algorithm.

[1]  Thomas Erlebach,et al.  Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs , 2006, APPROX-RANDOM.

[2]  Andrei V. Gagarin,et al.  Upper Bounds for α-Domination Parameters , 2009, Graphs Comb..

[3]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning , 1991, Oper. Res..

[4]  My T. Thai,et al.  On the approximability of positive influence dominating set in social networks , 2014, J. Comb. Optim..

[5]  Ryan A. Rossi,et al.  The Network Data Repository with Interactive Graph Analytics and Visualization , 2015, AAAI.

[6]  Anne Condon,et al.  Experiments with parallel graph coloring heuristics and applications of graph coloring , 1993, Cliques, Coloring, and Satisfiability.

[7]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[8]  Andrei V. Gagarin,et al.  Randomized algorithms and upper bounds for multiple domination in graphs and networks , 2013, Discret. Appl. Math..

[9]  Aric Hagberg,et al.  Exploring Network Structure, Dynamics, and Function using NetworkX , 2008, Proceedings of the Python in Science Conference.

[10]  Geng Lin,et al.  An ILP based memetic algorithm for finding minimum positive influence dominating sets in social networks , 2018, Physica A: Statistical Mechanics and its Applications.

[11]  Matthew Rink,et al.  Positive Influence Dominating Set generation in social networks , 2015, 2015 International Conference on Computing and Network Communications (CoCoNet).

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

[13]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Béla Bollobás,et al.  Random Graphs: Notation , 2001 .

[15]  Jean E. Dunbar,et al.  alpha-Domination , 2000, Discret. Math..

[16]  Boleslaw K. Szymanski,et al.  Dominating Scale-Free Networks Using Generalized Probabilistic Methods , 2014, Scientific reports.

[17]  Andrei V. Gagarin,et al.  Upper bounds for alpha-domination parameters , 2008, ArXiv.

[18]  Ning Chen,et al.  Approximation for Dominating Set Problem with Measure Functions , 2012, Comput. Artif. Intell..

[19]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[20]  Yan Shi,et al.  On positive influence dominating sets in social networks , 2011, Theor. Comput. Sci..

[21]  C. Greaves,et al.  Supporting behaviour change for diabetes prevention , 2010 .

[22]  Richard M. Karp,et al.  Algorithms for graph partitioning on the planted partition model , 2001, Random Struct. Algorithms.

[23]  Adriana Dapena,et al.  Calculation of the Connected Dominating Set Considering Vertex Importance Metrics , 2018, Entropy.

[24]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[25]  Christian Laforest,et al.  Hardness results and approximation algorithms of k-tuple domination in graphs , 2004, Inf. Process. Lett..

[26]  Nathaniel Charlton,et al.  Weighted Alpha-Rate Dominating Sets in Social Networks , 2014, 2014 Tenth International Conference on Signal-Image Technology and Internet-Based Systems.

[27]  Yin Tat Lee,et al.  Efficient Inverse Maintenance and Faster Algorithms for Linear Programming , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[28]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[29]  Lonnie Athens ‘Domination’ , 2002 .