Intermediate State - Advanced Data Structures and Algorithms - Quiz, Exercises of Data Structures and Algorithms

Main points of this past exam are: Advanced Data Structures, Intermediate State, Dinic's, Algorithm, Dynamic Trees, Residual Graph, Pathset Data Structure, Heavy Edges, Expose Operation, Light Edges

Typology: Exercises

2012/2013

Uploaded on 03/23/2013

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1. (5 points) The diagram below shows an intermediate state in the execution of Dinic’s
algorithm with dynamic trees (the tree edges are shown in bold and the costs are written
next to the vertices). Draw the residual graph that corresponds to this flow.
CS 542 – Advanced Data Structures and Algorithms
Quiz 5
Jonathan Turner 4/11/2012
a
b
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h
g
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t
1,1 2,2
1
4,4
2,0
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1
2,2
3,-
3,-
4,0
3,3
6,-
5,-
1,1
3,-
H
2 1
H 1
2
H
3,-
cost
4,-
pf2

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  • 1 -
  1. ( 5 points) The diagram below shows an intermediate state in the execution of Dinic’s algorithm with dynamic trees (the tree edges are shown in bold and the costs are written next to the vertices). Draw the residual graph that corresponds to this flow. CS 542 – Advanced Data Structures and Algorithms Quiz 5 Jonathan Turner 4/11/ a b c d s h g f e t

H

H^1

H

cost 4,-

  • 2 -
  1. ( 5 points) In the analysis of the pathset data structure, we introduced the notion of heavy and light edges. In the tree below, mark the heavy edges with an X. Suppose we do an expose operation at node u on a pathset with 500 vertices. Give an upper bound on the number of light edges in the path containing u immediately after the expose.

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