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CMPSCI 611: Advanced Algorithms Micah Adler
 

Summary: CMPSCI 611: Advanced Algorithms
Micah Adler
Problem Set 4 Out: November 14, 2002
Due: November 21, 2002
1. (a) Recall the Maximum Weight Forest (MWF) and Minimum Spanning Tree (MST) problems. De ne
appropriate decision problems for MWF and MST, and demonstrate that MWF P MST.
(b) A natural attempt to show that Max-Cut P Min-Cut would be a reduction of the following sort:
Given G, k as input to the Max-Cut problem, produce an input to the Min-Cut problem G 0 , k 0 , where
G 0 is the complement of G (i.e., there is an edge between u and v in G 0 if and only if there is no edge
between u and v in G.) Describe why this approach does not work.
(c) Show that Max-Cut P Min-Cut if and only if P = NP.
2. Show that if SAT 2 P, then, given a Boolean formula, we can nd a satisfying assignment to that
formula (if one exists) in polynomial time. Keep in mind that SAT is a decision problem, but you are
being asked to nd an actual assignment.
3. [CLRS] 34-3: Graph coloring.
4. Consider the 1
3
-Clique problem:
Input: A graph G.
Question: Does G have a Clique of size exactly dn=3e, where n is the number of nodes in G?

  

Source: Adler, Micah - Department of Computer Science, University of Massachusetts at Amherst

 

Collections: Computer Technologies and Information Sciences