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Unformatted text preview: CSIS 0250B Design and Analysis of Algorithms Assignment 4 Due: 11:55 PM, Apr 2, 2009 Below we assume that all networks have integer edge capacities, and the flow being considered have integer value. In our analysis, you can express the time complexty in terms of the notation MFT( n,m ), which denotes the time complexity of a finding the maximum flow from a source s to a sink t in a network with n verteices and m edges. Warm-up – No need to turn in. 1. True or false. Let G be an arbitrary flow network, with a source s , a sink t , and a positive integer capacity c e for every edge. Let ( A,B ) be a minimum s-t cut of G . Now suppose we add 1 to every edge capacity; then ( A,B ) is still a minimum s-t cut. 2. True or false. Let G be a flow network. A maximum flow f of G is given in advance. Suppose that the capacity of a particular edge e of G increases by 1. Let G be the new network. The maximum flow of G has a value equal to value ( f ) or value ( f ) + 1. 3. Let G be a flow network. In addition to edge capacities, each node v (other than source s and sink t ) has a node capacity c ( v ). A flow has to satisfy the extra constraint that the total inflow)....
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This note was uploaded on 03/01/2010 for the course CS 1234 taught by Professor Chan during the Spring '10 term at University of the Bío-Bío.
- Spring '10