1. A graph G = (V, E) is called bipartite if the vertex set can be partitioned into sets
X, Y such that no edge in E has both endpoints in the same set X or Y . Give a linear
time algorithm to check if a graph is bipartite.
2. A graph is 2 vertex connecte
Aug 2, 2010
Review DFS. Run DFS on example graph and show back edges, and label each vertex
with the time at which it is visited.
Given an undirected graph, call a vertex critical if its removal disconnects the graph.
Give a linear time
Aug 13, 2010
Suppose you want to go from city A to city B on a long highway. Once you ll your
car tank to full capacity, it can travel D kilometres. There are several locations on the
highway which have petrol pumps. Assume that there i
Aug 9, 2010
Review DFS on directed graphs.
Given an undirected graph, we say it is bipartite if we can partition the vertex set into
two disjoint sets A and B such that all edges go between A and B. Give a linear time
algorithm to chec
Due on : November, 2010
1. You are given a directed graph with edge capacities, and two vertices s and t. Let A
and B be two dierent st min-cuts. Is A B also a min-cut between s and t ? How
about A B ? Give reasons for your answer. How w
Due on : September 3, 2010
1. You are given a line with n points, labeled 1 to n, marked on it. You are also given a
set of intervals I1 , . . . , Ik , where interval Ii is of the form [si , ei ], 1 si ei n. Find
a set of points X of sm
Due on : September 24, 2010
1. (a) Suppose we are given two sorted arrays A[1 . . . n] and B[1 . . . n] and an integer k.
Describe an algorithm to nd the k th smallest element in the union of A and B in
O(log n) time. For example, if k
Due on : October 21, 2010
1. You are given a set of intervals, I1 , . . . , Ik , where each interval Ii = [si , ei ] has an
associated prot pi . Give an ecient algorithm for nding a subset of intervals of
maximum total prot satisfying t
Due on : August 20, 2010
1. We say that a directed graph is nice if for every pair of vertices u and v in the graph,
either u is reachable from v or v is reachable from u. Give a linear time algorithm to
check if a graph is nice.