Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks

Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully investigated by maximum entropy method application. In this paper we prove a theorem that establishes asymptotic properties of the maximum entropy routing solution. This result, besides being theoretically interesting, can be used to direct initial approximation for iterative optimization algorithms and to speed up their convergence.

[1]  Seyed Mostafa Hosseinalipour,et al.  Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet , 2011 .

[2]  Milan Tuba.  An algorithm for the network design problem based on the maximum entropy method , 2010 .

[3]  Shinya Shiotani,et al.  Neutron powder diffraction and difference maximum entropy method analysis of protium- and deuterium-dissolved BaSn0.5In0.5O2.75+α , 2009 .

[4]  Beongku An,et al.  An entropy based cooperative-aided routing protocol for mobile ad-hoc networks , 2011, 2011 Third International Conference on Ubiquitous and Future Networks (ICUFN).

[5]  A. Shamilov.  Generalized entropy optimization problems and the existence of their solutions , 2007 .

[6]  Rui A. P. Perdigão,et al.  Minimum Mutual Information and Non-Gaussianity Through the Maximum Entropy Method: Theory and Properties , 2012, Entropy.

[7]  Kara M. Kockelman,et al.  Maximum Entropy Method for Subnetwork Origin–Destination Trip Matrix Estimation , 2010 .

[8]  Anisa T. Bajkova.  Reconstructing Images from Projections Using the Maximum-Entropy Method. Numerical Simulations of Low-Aspect Astrotomography , 2007 .

[9]  Xuan Wang,et al.  A Maximum Entropy Approach to Chinese Pin Yin-To-Character Conversion , 2006, 2006 IEEE International Conference on Systems, Man and Cybernetics.

[10]  YU Tai-Peng.  IMPROVEMENT ON THE MODIFIED MAXIMUM ENTROPY METHOD FOR TEXTURE ANALYSIS BY PARTICLE SWARM OPTIMIZATION , 2009 .

[11]  Masaki Murata,et al.  Using the Maximum Entropy Method for Natural Language Processing: Category Estimation, Feature Extraction, and Error Correction , 2010, Cognitive Computation.

[12]  Imre Csiszár,et al.  Axiomatic Characterizations of Information Measures , 2008, Entropy.

[13]  J. J. Dahlgaard,et al.  Simultaneous Equation Model based on the generalized maximum entropy for studying the effect of management factors on enterprise performance , 2009 .

[14]  B. Iversen,et al.  Maximum-entropy-method charge densities based on structure-factor extraction with the commonly used Rietveld refinement programs GSAS, FullProf and Jana2006. , 2012, Acta crystallographica. Section A, Foundations of crystallography.

[15]  Xue Wang,et al.  Parallel energy-efficient coverage optimization with maximum entropy clustering in wireless sensor networks , 2009, J. Parallel Distributed Comput..

[16]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[17]  Beongku An,et al.  An Entropy-based Routing Protocol using Mobility in Mobile Ad-hoc Wireless Sensor Networks , 2009, 2009 11th International Conference on Advanced Communication Technology.

[18]  Milan Tuba.  Plenary lecture 4: maximum entropy method and underdetermined systems applied to computer network topology and routing , 2009 .

[19]  Amir Hossein Darooneh,et al.  Tsallis Entropy, Escort Probability and the Incomplete Information Theory , 2010, Entropy.

[20]  Francisco J. Tapiador,et al.  A Maximum Entropy Modelling of the Rain Drop Size Distribution , 2011, Entropy.

[21]  Milan TUBA.  Guided MaximumEntropy Method Algorithm for the Network Topology and Routing , 2011 .