CMSC 641, Fall 1996
Design and Analysis of Algorithms

Computer Science & Electrical Engineering Department
University of Maryland Baltimore County

Assignments

• Homework 1
• Homework 2
• Homework 3 (NOTE: THERE ARE NO MODIFICATIONS TO THE STATEMENT OF PROBLEM 2.)
• Solution to Homework 3
• Carefully justify that the actual cost of CONSOLIDATE in FIB-HEAP-EXTRACT-MIN is O(D(n)+t(H)) when called on an n-node fib-heap H.
• Homework 4: Do Exercise 23.2-7 and Problem 23-2 from the text.
• NOTE-1: Part (b) of Problem 23-2 changes as follows: Let G=(V,E) be a connected undirected graph, and let D=(V,T) be a DFS tree of G. Prove that a vertex v of G, that is not the root of D, is an articulation point of G if and only if there exists a child u of v (in D) such that there is no back edge in G between any node in the subtree of D rooted at u and some proper ancestor of v.
• NOTE-2: The deadline for Homework 4 is Nov 11, 1996.
• Project
• A Sample C program to generate test matrices for the Project.
• Before you use the matrix from the program above, you need to adjust it so that it is symmetric and with 0 on the main diagonal (so that it corresponds to an undirected graph for questions (v)-(vi) of the project). This can be done as in the this program.
• Homework 5 (40 points). Due Nov 27, 1996. Let G=(V,E) be an undirected connected graph, and let c:E-->R be a function assigning (non-negative) capacities to the edges of G. Define the capacity of a path p in G to be equal to the minimum of the capacities of the edges along that path p. The All-Pairs Largest Capacity Paths problem is, given G and c as above, to find largest capacity paths between all pairs of vertices of G.
  1. Design an optimal algorithm for the All Pairs Largest Capacity Paths problem.
  2. Prove that your algorithm is correct and analyze its computational complexity.
  3. Design and analyze the fastest algorithm you can that solves the Single-Source Largest Capacity Paths problem.
• Solution (Outline) to Homework 5.