By A. K. Amoura, E. Bampis, C. Kenyon, Y. Manoussakis (auth.), Rainer Burkard, Gerhard Woeginger (eds.)
This ebook constitutes the refereed court cases of the fifth Annual overseas eu Symposium on Algorithms, ESA'97, held in Graz, Austria, September 1997.
The 38 revised complete papers offered have been chosen from 112 submitted papers. The papers tackle a huge spectrum of theoretical and applicational points in algorithms thought and layout. one of the themes coated are approximation algorithms, graph and community algorithms, combinatorial optimization, computational biology, computational arithmetic, info compression, allotted computing, evolutionary algorithms, neural computing, on-line algorithms, parallel computing, trend matching, and others.
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Additional resources for Algorithms — ESA '97: 5th Annual European Symposium Graz, Austria, September 15–17, 1997 Proceedings
In terms ofN, how many additions are performed during this calculation? Given this. what is the complexity order of this algorithm? Note that all the work here is performed by the recursive function G and that F exists only to set the correct initial values of the parameters A and B. This is a common technique in recursive programming and will reappear in Chapter 7. 3-9. [Mathematically oriented] The constant ip referred to in the text is called the "golden ratio" and has considerable significance.
As N grows. the number of additions required to compute FIB(N) by this mechanism increases fairly quickly. Although we as yet have only circumstantial evidence for this conjecture (see Exercise 3-7). it appears that the number of additions required to compute FIB(N) is given by the formula FIB(N+l) - 1 By applying some additional mathematics. 618034 The details of this derivation are largely irrelevant to understanding the computational complexity that this implies and have been left to the mathematically inclined reader as Exercise 3-9.
In almost all instances. are calculated using 2 as the logarithmic base. For the rest of this text. we will follow the standard convention in computer science and use "log N" to indicate base 2 logarithms without explicitly writing down the base. 23 Mathematical Preliminaries Estimates of computational complexity are most often used to provide insight into the behavior of an algorithm as the size of the problem grows large. Here, for example, we can use the worst-case formula to create a table showing the number of guesses required for the linear and binary search algorithms, respectively: N Linear search 10 100 1,000 10,000 100,000 1,000,000 10 100 1,000 10,000 100,000 1,000,000 Binary search 4 7 10 14 17 20 This table demonstrates conclusively the value of binary search.