Lectures‎ > ‎

### Lecture 04

For today you should:
1) Swap books, read your predecessor's summary, read another chunk and write a summary.  If you get an unread book, you might have to create the page for it.
2) Start Chapter 2?

Today:
1) Swappy books: any ideas for replicable experiments?
2) Results from Chapter 1.
3) Intro to Chapter 2.
4) Studio time.

For next time you should:
1) Read Chapter 2 and prepare the reading questions from Lecture 3.
2) Work on Exercises from Chapter 2.
3) Bring back your swappy book.
4) Extra time?  Catch up, get ahead, skim Complexity Digest for case study ideas.

### Erdos-Renyi Random Graphs

Why did Erdos and Renyi study this problem?  Skim the papers and see if you can tell.

Why did I include this example?
1) Chance to practice graph algorithms and see something interesting.
2) First example of critical behavior, which will be a recurring theme.
3) Connection to percolation, which we will come back to (and from there on to fractals).
4) Candidate model of real phenomena.

Caveat from Wikipedia:
Both of the two major assumptions of the G(np) model (that edges are independent and that each edge is equally likely) may be inappropriate for modeling real-life phenomena. In particular, an Erdős–Rényi graph does not have heavy tails, as is the case in many real networks. Moreover, it has low clustering, unlike many social networks. For popular modeling alternatives, see Barabási–Albert model and Watts and Strogatz model. A model for interacting ER networks was developed recently by Buldyrev et al[5].

### Analysis of Algorithms

How can we compare algorithms when their performance depends on hardware, size of the input, and contents of the input?

How do you compare two functions to say which is bigger?

if

Because O(g(x)) is a set, it is more correct to write "element of" rather than "equals".

This definition implies some of the limitations of this kind of analysis:
1) Only relevant for large x.
2) M can be arbitrarily big.