# Design Analysis Of Algorithm

### Maximum Bipartite Matching

5 min read

Maximum bipartite matching: Some combinatorial problems can easily be cast as maximum-flow problems. The multiple-source, multiple-sink maximum-flow problem from Section 26.1 gave us one example. There are other combinatorial problems that seem on the surface to have little to do with flow networks, but can in fact be reduced to maximum-flow problems. This section presents one such problem: finding a maximum matching in a bipartite graph (see Section B.4). In order to solve this problem, we shall take advantage of an integrality property provided by the Ford-Fulkerson method. We shall also see that the Ford-Fulkerson method can be made to solve the maximum-bipartite-matching problem on a graph

*G*= (*V*,*E*) in*O*(*V E*) time. Given an undirected graph*G*= (*V*,*E*), a**is a subset of edges***matching**M*⊆*E*such that for all vertices*v*∈*V*, at most one edge of*M*is incident on*v*. We say that a vertex*v*∈*V*is**by matching***matched**M*if some edge in*M*is incident on*v*; otherwise,*v*is**. A***unmatched***is a matching of maximum cardinality, that is, a matching***maximum matching**M*such that for any matching*M*', we have |*M*| ≥ |*M*'|. In this section, we shall restrict our attention to finding maximum matchings in bipartite graphs. We assume that the vertex set can be partitioned into*V*=*L*∪*R*, where*L*and*R*are disjoint and all edges in*E*go between*L*and*R*. We further assume that every vertex in*V*has at least one incident edge. Figure 26.7 illustrates the notion of a matching.### The Dft And Fft

3 min read

Lemma 30.6: (Summation lemma) For any integer

*n*≥ 1 and nonnegative integer*k*not divisible by*n*,**Equation (A.5) applies to complex values as well as to reals, and so we have***Proof*Basic Electrical Engineering

Automobile Engineering

Maths for Engineers - 1

Human Values & Prof. Ethics-1

Operations Research

Quality Control Engineering

Six Sigma

Total Quality Management (TQM)

Maths for Engineers - 2

Physics for Engineers - 2

Maths for Engineers - 3

Graph Theory

Physics for Engineers - 1

Control Systems - 1

Neural Network & Fuzzy Systems

Real Time Systems

Automata | Comp. Sc. Engg.

Data Mining & Data Warehousing

Numerical Methods

Mechatronics

Artificial Intelligence

Design Analysis of Algorithm

Discrete Mathematics

Automobile Engineering

Maths for Engineers - 1

Human Values & Prof. Ethics-1

Operations Research

Quality Control Engineering

Six Sigma

Total Quality Management (TQM)

Maths for Engineers - 2

Physics for Engineers - 2

Maths for Engineers - 3

Graph Theory

Physics for Engineers - 1

Control Systems - 1

Neural Network & Fuzzy Systems

Real Time Systems

Automata | Comp. Sc. Engg.

Data Mining & Data Warehousing

Numerical Methods

Mechatronics

Artificial Intelligence

Design Analysis of Algorithm

Discrete Mathematics