AlgMidTermFall2006

AlgMidTermFall2006 - Algorithms CSE5811 MidTerm Fall2006...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Algorithms CSE5811 MidTerm Fall2006 Points 40 Time 70 min 1. Describe what does the following algorithm produce, and analyze its asymptotic time- complexity. [For analyzing complexity, presume n = 2 k , for some positive integer k .] Algorithm Unknown (rational a , positive int n ) If n = = 1 return a Else If n %2 = = 0 then Return Unknown ( a , n /2)* Unknown ( a , n /2) Else Return a * Unknown ( a , ( n -1)/2)* Unknown ( a , ( n -1)/2) End algorithm. 2. For a weighted undirected graph G a culprit set C of arcs has the following property: if all the elements of C are removed from G it becomes acyclic (tree), and a min-culprit set M of arcs is such that the aggregate weight of arcs in M is minimum for all such sets C . Write a greedy algorithm to find M given a graph G . [Hint: First try to find appropriate G M .] 3a. The following is a directed graph G : [ a: b , d ], [ b: c ], [ c: a ], [ d: e ], [ e: f ], [ f: d ], where [ a: b , d ] means there is a directed arc in G from a to b and from a to d . Draw G . You are to find the strong connected components (SCCs) of the graph by running the relevant algorithm. Show (i) the first DFS-spanning tree of G starting with the node a , along with the post-order traversal numbers; (ii) the post-order traversal numbers shown on the nodes of the reverse graph G’ ; and (iii) the second set of DFS spanning trees on the reverse graph G’ , which identifies the SCCs of
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

AlgMidTermFall2006 - Algorithms CSE5811 MidTerm Fall2006...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online