Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

C-13.21
Computer networks should avoid single points of failure, that is, network nodes
that can disconnect the network if they fail. We say a connected graph G is
biconnected if it contains no vertex whose removal would divide G into two or
more connected components. Give an O(n + m)-time algorithm for adding at
most n edges to a connected graph G, with n ≥ 3 vertices and m ≥ n − 1 edges,
to guarantee that G is biconnected.
C-13.22
NASA wants to link n stations spread over the country using communication
channels. Each pair of stations has a different bandwidth available, which is
known a priori. NASA wants to select n − 1 channels (the minimum possible) in
such a way that all the stations are linked by the channels and the total
bandwidth (defined as the sum of the individual bandwidths of the channels) is
maximum. Give an efficient algorithm for this problem and determine its worstcase
time complexity. Consider the weighted graph G = (V,E), where V is the
set of stations and E is the set of channels between the stations. Define the
weight w(e) of an edge e in E as the bandwidth of the corresponding channel.
C-13.23
Suppose you are given a timetable, which consists of:
•
A set A of n airports, and for each airport a in A, a minimum connecting
time c(a).
•
A set F of m flights, and the following, for each flight f in F:
˚
Origin airport a 1 (f) in A
˚
Destination airport a 2 (f) in A
˚
Departure time t 1 (f)
˚
Arrival time t 2 (f).
877