CHAPTER 23
Minimum Spanning Trees
Dec 2015
In the design of electronic circuitry, it is often necessary to
make the pins of several components electrically equivalent by
wiring them together. To interconnect a set of n pins, we can
use an arrangement of n
Lecture 7: Basics of Data Structures
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 17, 2016
Introduction
Arrays
Contiguous vs. Linked Data Structures
Linked
Extra
Lecture 10: Elementary Sorts
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 30, 2016
Introduction
Elementary Sorts
Introduction
Sorting is a very critical operation
Lecture 6: Introduction to Data Structures
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 16, 2016
Introduction
What is a data structure?
Data structures organise (
Matching Theory
Matching:
Let G = (V , E ) be a simple graph. A subset M of E is called a
matching in G if no pair of edges e1 and e2 of M share a
common vertex.
M E is called a matching in G if, for every pair of edges
(u , v ) and (p, q ) of M , cfw_u ,
Graph Theory
A NPTEL Course
S.A. Choudum
Department of Mathematics
IIT Madras
Chennai, India
email: sac@iitm.ac.in
Notes to the Reader
At a faster pace the course can be read in about 65 lectures and at a slower
pace in about 100 lectures.
By skipping cer
Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-5
1. Let G be a bipartite graph. Prove that G has a matching of size at least |E (G)|/ (G).
2. Let = cfw_S1 , S2 , . . . Sr be a familly of distinct non
Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-4
1. Every k -connected graph G has atleast
nk
2
edges.
2. If G is 3-regular, then (G) = (G). Does it hold for multi-graphs?
3. Let r, s, t be positive i
Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-3
(1) Let T be a tree such that d(v ) cfw_5, 4, 3, 1, 1, . . . , 1, for each vertex v in T . Find the
number of leaf vertices (vertices of degree 1) in T
Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-2
Notations: n is the number of vertices and m is the number of edges in a graph G = (V, E ).
(1) Let A = (aij ) be the adjacency matrix of a graph G. Sh
Indian Institute of Technology Madras
Department of Mathematics
MA 2130 Basic Graph Theory
Assignment-I
Notations and Denitions:
(1) (G) = mincfw_d(v ) : v V (G), (G) = maxcfw_d(v ) : v V (G).
(2) The distance d(u, v ) between a pair of vertices u, v V (G
Lecture 12: Insertion, Faster Sorts
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
September 6, 2016
Insertion Sort
Overview
Divide and Conquer
Merge Sort
Quick Sort
Other
Lecture 4: Analysis of Algorithms
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 8, 2016
Introduction
Analysis of Algorithms
Order of Growth
Which of these algorith
Lecture 0: Administrivia/Introduction
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 1, 2016
Administrivia
Logistics
Lectures:
Labs:
Venue:
E-mail:
Oce:
Oce hours:
Monte Carlo Simulation and Resampling
Tom Carsey (Instructor)
Jeff Harden (TA)
ICPSR Summer Course
Summer, 2011
Monte Carlo Simulation and Resampling
1/68
Resampling
Resampling methods share many similarities to Monte Carlo
simulations in fact, some refe
CHAPTER 25
All-Pairs Shortest Paths
April 2015
25.2 The Floyd-Warshall algorithm
We will use a different dynamic-programming formulation
to solve the all-pairs shortest-paths problem on a directed
graph G = (V, E). The resulting algorithm, known as the
Fl
CSE 5311 Homework 5 Solution
Problem 25.1-3
What does the matrix
L(0)
0
0
= 0
.
.
.
.
.
.
.
.
0
.
.
.
.
.
.
used in the shortest-paths algorithms correspond to in regular matrix multiplication?
Answer
The matrix L(0) corresponds to the
1
0
I = 0
.
3.3. Asymptotic Analysis
3.3
123
Asymptotic Analysis
In algorithm analysis, we focus on the growth rate of the running time as a function
of the input size n, taking a big-picture approach. For example, it is often enough
just to know that the running tim
BT 3051 Data Structures and Algorithms for Biology
JulNov 2016
Self-assessment Exercises
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
Last updated: September 2, 2016
In this document, I outline some interesting self-asse
BT 3051 Data Structures and Algorithms for Biology
JulNov 2016
Assignment 2: Object-oriented Programming
14th September 2016
Due date: 21st September, 2016 @ 17:00
Maximum marks: 50
Instructions: Write Python codes to solve the problems mentioned below. I
BT 3051 Data Structures and Algorithms for Biology
JulNov 2016
Assignment 1
16th August 2016
Due date: 23rd August, 2016 @ 17:00
Maximum marks: 20
Instructions: Write Python codes to solve the problems mentioned below. If you need any assistance,
feel fre
Lecture 1: Overview
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 2, 2016
Overview
What is an algorithm?
Courtesy: Chris Lacher, Florida State University (CIS 4930
Lecture 2: Introduction to Algorithms
BT 3051 Data Structures and Algorithms for Biology
Karthik Raman
Department of Biotechnology
Indian Institute of Technology Madras
August 3, 2016
Introduction
Examples
What is an algorithm?
Courtesy: Chris Lacher, Flo
BT 3051 Data Structures and Algorithms for Biology
JulNov 2016
Assignment 0
9th August 2016
Due date: 12th August, 2016 @ 17:00
Maximum marks: 15
Instructions: Write Python codes to solve the problems mentioned below. If you need any assistance,
feel free