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Algorithm Theory: Finding Paths with Max Success Probability in Directed Graphs, Exercises of Algorithms and Programming

Aliah UniversityAlgorithms and Programming

Information about problems to be covered in a problem session for cos 423: theory of algorithms, focusing on finding paths with the highest success probability in a directed graph with associated success probabilities for each edge, spring 2005.

Typology: Exercises

2011/2012

Uploaded on 07/16/2012

santhanakrishnan
santhanakrishnan 🇮🇳

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COS 423 Theory of Algorithms Spring 2005
Precept 2
Here are the problems that we plan to work out in the problem session.
1. Problem 4.12.
2. Chapter 4, solved exercise 3.
3. Let G=(V,E) be a directed graph, and let sbe a distinguished node. Each edge (u, v) has an
associated success probability γuv between 0 and 1. When sending a message from ualong an edge
(u, v), the message arrives at vwith probability γuv and is dropped with probability 1 −γuv.Your
goal is to find a path from sto vwith the highest success probability. Assume that the failure events
are independent so that the success probability of a path is the product of the probabilities of its
constituent edges.
1
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COS 423 Theory of Algorithms Spring 2005

Precept 2

Here are the problems that we plan to work out in the problem session.

  1. Problem 4.12.
  2. Chapter 4, solved exercise 3.
  3. Let G = (V, E) be a directed graph, and let s be a distinguished node. Each edge (u, v) has an associated success probability γuv between 0 and 1. When sending a message from u along an edge (u, v), the message arrives at v with probability γuv and is dropped with probability 1 − γuv. Your goal is to find a path from s to v with the highest success probability. Assume that the failure events are independent so that the success probability of a path is the product of the probabilities of its constituent edges.

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