final-09 - AMS/MBA 546 (Spring, 2009) Estie Arkin Network...

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AMS/MBA 546 (Spring, 2009) Estie Arkin Network Flows - Final Do 4 of the following 6 problems. You are permitted to use the text (AMO), your notes and any material handed out in class. The exam time is 2 hours and 30 minutes. GOOD LUCK!!! Academic integrity is expected of all students at all times, whether in the presence or absence of members of the faculty. Understanding this, I declare that I shall not give, use, or receive unauthorized aid in this examination. Name (PRINT CLEARLY), and Signature: Problems to be graded: 1). (a). A Feedback edge set of an undirected graph G = ( N,E ) is a subset of edges E E whose removal results in an acyclic graph G = ( N,E \ E ). Given a graph with positive edge weights w ij > 0, describe a polynomial time algorithm that Fnds a minimum weight feedback edge set. Recall, this problem is NP Complete for directed graphs. (b). ±or a graph G = ( N,E ) deFne conn ( G ) the number of connected components of G . Prove that conn ( G ) + m n for every graph G . | N | = n , and | E | = m . Comment: parts (a) and (b) are not related.
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This note was uploaded on 01/31/2011 for the course AMS 546 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.

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final-09 - AMS/MBA 546 (Spring, 2009) Estie Arkin Network...

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