Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 20.3, Problem 5E
Program Plan Intro
To explain the running time of the vEB tree created by
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Suppose there are six cities in a state. The distance matrix between each pair of the cities is given below.
What is the dendrogram generated by hierarchical clustering with single-linkage?
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Based on the resulting dendrogram, if we want to create 4 clusters, they are
Cluster Number
Items
1
Let G = (V, E) be a DAG, where every edge e = ij and every vertex x have positive weighs w(i,j) and w(x), respectively, associated with them. Design an algorithm for computing a maximum weight path. What is the time complexity of your algorithm? (You must start with the correct definitions, and then write a recurrence relation.)
For the k-means algorithm, it is interesting to
note that by choosing the initial cluster centers
carefully,
we may be able to not only speed up the
convergence of the algorithm, but also
guarantee the quality
of the final clustering. The k-means++
algorithm is a variant of k-means, which
chooses the initial
centers as follows. First, it selects one center
uniformly at random from the objects in the data
set.
Iteratively, for each object p other than the
chosen center, it chooses an object as the new
center. This
object is chosen at random with probability
proportional to dist(p)2, where dist(p)) is the
distance
from p) to the closest center that has already
been chosen. The iteration continues until k
centers are
selected.
Explain why this method will not only speed up
the convergence of the k-means algorithm, but
also
guarantee the quality of the final clustering
results
jo 9:15
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