April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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488 Design and Analysis of Algorithms
From a practical view point, an approximate solution to an optimization problem, which is not truly
optimal but very near to it, is quite useful. Algorithms designed taking into account this fact are called
Approximation Algorithms. A limited set of such problems is the numerical algorithms to calculate values
of functions like sine, cosine, and so on.
Some of the approximation algorithms are guaranteed to produce results quite close to the optimum
results. For example, there is an algorithm for TSP, which takes O(n
3
) time and guarantees that the tour length
is not more than 1.5 times the optimum (which is not known). In fact, a much simpler algorithm, based on
fi nding a MST for the graph and traversing ...
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