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CS 473: Fundamental Algorithms, Spring 2012
Homework 6 (due Tuesday, 23:55:00, March 13, 2012)
See homework 1.
Each student individually have to also do
quiz 6
online.
Version:
1.11
1. (
30 pts.
)
An Improved Algorithm for MST.
Consider Bor˚
uvka’s algorithm for
MST
as seen in the discussion. Consider a modiﬁed al
gorithms for
MST
that works as follows. It runs Bor˚
uvka’s algorithm for some number of
iterations and then switches to Prim’s algorithm (with Fibonacci’s heaps). Show that by
appropriately choosing the switching point, one can obtain an algorithm for
MST
with run
ning time
O
((
m
+
n
) log log
n
). Describe and analyze the algorithm. Don’t forget to prove
correctness.
2. (
30 pts.
)
Amortized Analysis
Recall from class the idea of PathCompression in the UnionFind data structure for maintain
ing disjoint sets. Prove that if PathCompression is used then the total time for
k
operations
in which all the
union
operations precede all the
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 Spring '08
 Chekuri,C
 Algorithms

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