UMBC CMSC441, Design & Analysis of Algorithms, Fall 2014

Homework 9

Due Thursday, October 30, 2014

  1. Choke Point.
    Let G = (V, E) be an undirected graph represented as an adjacency list. Fix two vertices s and t. A choke point for s and t is a vertex c whose removal will disconnect s from t.
    1. Argue that if the shortest path from s to t has length strictly greater than V/2, then G must have a choke point for s and t.
    2. Devise an algorithm to find a choke point in this case. Describe your algorithm at a high level (try to avoid pseudocode). For full credit, your algorithm must run in O(V + E) time.
    3. State and briefly justify the running time of your algorithm.

  2. Semi-connected directed graphs. Exercise 22.5-7, page 621.
    Note: The "or" in the definition of semi-connected is inclusive. That is, a semi-connected graph is allowed to have both a path from u to v and a path from v to u.

  3. Alternative MST algorithms. Problem 23-4, page 641.

Last Modified: 23 Oct 2014 08:14:01 EDT by Richard Chang
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