Any more paths to Augument ? Let us see the
The residual network has the same vertices as the
original network, and one or two edges for each
edge in the original.
if the flo
Overall minimum cut
The minimum cut between two specified nodes
can be obtained as a byproduct of the maximum
flow computation. If, however, we want an
overall minimum cut in the whole graph, then a
single maximum flow computation does not
Minimum Cut Problem
Abstraction for material flowing through the edges.
G = (V, E) = directed graph, no parallel edges.
Two distinguished nodes: s = source, t = sink.
c(e) = capacity of edge e.
Integer Linear Programming - Introduction
In many network planning problems the variables can take only
integer values, because they represent choices among a finite
number of possibilities.
Such a mathematical program is known as integer program.
An Optimization Problem in Cellular Network Design:
Formulation via Integer Linear Program
In cellular networks the coverage area is divided into cells. Each
cell is served by base station to which the mobile units connect
The base stations ar
Branch and Bound - Complete Enumeration
Systematically considers all possible values of the decision
If there are n binary variables, there are 2n different
Usual idea: iteratively break the problem in two. At the
first iteration, we c
The Maximum Flow Problem
The historically first and most fundamental
network flow problem is the Maximum
The Maximum Flow Problem
Given a network with N nodes and links among them.
We would like to transport some entity (for example
Randomized rounding contd.
We can solve the LP relaxation by any LP algorithm, which
generally results in variable assignments that are between 0 and
The next step is to round the variables to 0/1 values. This could
be done dete
ILP Solution Techniques
Consider an arbitrary ILP problem:
cTxj = z
Subject to: Axj b
Xj is integer j = 1, 2, . . . , n
Notice that if we drop (or relax) the integrality constraint, we
are left with an LP problem. This is called the L
Example 2: Fixed Charge Problem
A telecom company wants to offer new services to its
customers. Each service can be offered in different amounts
(e.g., with different bandwidth). The goal is to decide how much
of each service is to be offered to maximize
CS6385 Algorithmic Aspects of Telecommunication Networks, Section 001
Cross listed as TE 6385.
Fall Semester, 2015
Professor Contact Information
Name: Dr. Andras Farago, Professor
Department: Computer Science