Solution of a Linear Recurrence Equation Arising in Analysis of Some Algorithms
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چکیده
ABSlRACf .-1 [ ] We study a recurrence equation of type 1. ...(2/1.+1-2)=0... + L Z lkt n ~N where all k=l is any sequence and s • N are integers. This recurrence arises in many applications, e.g. investigating the average number of bit inspection for a random unsuccessful search by Patricia tree, analyzing the average conflict resolution interval for contention resolution algorithms in a broadcast communication environment, etc. We present a closed-form solution of the recurrence and then we establish an asymptotic approximation for it. In addition, we offer an approximation of a generating function, I (z), of 1,.. for small values of z .
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تاریخ انتشار 2013