503_HW4_S11 - s to x for some vertex x 3(14 points Chapter...

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UML CS Analysis of Algorithms 91.503 (section 201) Spring, 2011 page 1 of 1 Homework #4 Assigned: Tuesday, 2/22 Due: Tuesday, 3/8 start of lecture This assignment covers textbook material in Chapters 24-26 (Shortest Paths and Network Flow) and the conference paper “On calculating connected dominating set for efficient routing in ad hoc wireless networks.” 1. (40 points) Chapter 24 : Single-Source Shortest Paths (Nesting Boxes) : Problem 24- 2 on p. 678 (a)-(c). 2. (6 points) Chapter 25 : All-Pairs Shortest Paths ( Sedgewick ): Give an example of a directed, weighted graph that shows how we could know that a path from vertex s to vertex t is shortest without knowing the length of a shorter path from
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Unformatted text preview: s to x for some vertex x . 3. (14 points) Chapter 25 : Dominating Sets: In the paper “ On calculating connected dominating set for efficient routing in ad hoc wireless networks ” two rules for modifying the dominating set are presented on p. 9 of Section 3. a) Prove that applying Rule 1 to ' G to produce subgraph } { ' v G − results in } { ' v G − being a connected subgraph of ' G . b) Prove that applying Rule 2 to ' G to produce subgraph } { ' v G − results in } { ' v G − being a connected subgraph of ' G . 4. (40 points) Chapter 26 : Flow Networks ( Escape Problem ): Problem 26-1 on p. 760-761 (a)-(b)....
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