Exponential Life Time Binary Search Tree

Abstract

The random tree theory is useful in investigating the equivalent conductance of a random conductance network. Statistical considerations are introduced in network graph theory by replacing the exact average value of trees of the network by the average product of the conductance of a random sample of N-1 branches drawn without replacement from the population of B branches. The case of a binary distribution of conductance has treated and it was found that random trees theory is consistent with effective medium theory applied to the same case. It is supposed that these periods of times are independent identically distributed with exponential distribution with parameter 1. The essential focus is on the successful and unsuccessful searching. For the introduced random variables the mean is given, variance and asymptotic distribution. Law of large numbers is also established.