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Power Laws, Highly Optimized Tolerance and generalized source coding John Doyle, J.M. Carlson Presented by Sumitra Ganesh Overview Propose an optimization problem that is a generalization of the Data Compression (Source coding) problem Problem is formulated and analyzed for 3 examples : Data compression (DC), Website layout (WWW), Forest Fires (FF) The PLR optimization problem J { pi li | li f ( ri ), ri R} 1 i N pi Probability of event li ri Loss/size associated with event Resource allocated to suppress the size f (ri ) log(ri ), 0 f (ri ) c(ri 1) / , 0 Data Compression 0 Each source symbol – codeword of k p 2 Bits. i i l 2 1 i ri pi li log( pi ) ki J pi log( pi ) li Web Layout 1 The sizes are the lengths of the files The probabilities are determined by user interest in the files The cost is the average delay that a user experiences in downloading files Resource limit is on the total number of files WWW contd Crucial : The resource-loss tradeoff is determined by li ri 1 The resource allocation (separation if document into files) may change influence the hit probability for a given file. Split the one-dimensional file into N regions of equal size and with uniform access probability Forest Fires 1 Two-dimensional problem The losses are the burned areas The probabilities are determined by the probability of sparks The cost is the average timber lost in fires Resource is the density of firebreaks etc. Heavy tailed CDFs Comments Generalized framework : not clear about its applicability The average statistics seem to obey power laws even though the individual websites were not optimally designed (Why?) The three examples are explained well