Lecture 15 CSE 331 Oct 3, 2011

Mid term Next Monday in class Unfortunately I won’t be there Jiun-Jie with my PhD students Steve & Swapnoneel will proctor the exam

Feedback Response-I I’ll use the microphone today Let me know via poll on the blog if it worked better

Graphs will help us here Feedback Response-II Problem Statement Real world problem Graphs will help us here Problem Definition Precise mathematical def Algorithm “Implementation” Data Structures Analysis Correctness/Run time

Feedback Response-III The workload is “insane” and I might be unaware of it Syllabus states that you’re supposed to spend at least 8-12 hours outside of the lectures If you’re spending much more time than above, please come and talk to me I’m aware that ideal situations do not always exists More chances for you to “make-up” in the course

Mid term entry Has been posted on the blog Don’t read too much into the content of the sample mid-term

On Friday, Oct 7 hours-a-thon Atri: 2:00-3:00 (Bell 123) Jiun-Jie: 4:00-5:00 (Commons 9) Jesse: 5:00-6:00 (Bell 224)

Empty Slots Coming up…

Graph representations 1 Better for sparse graphs and traversals Adjacency matrix Adjacency List (u,v) in E? O(1) O(n) [ O(nv) ] All neighbors of u? O(n) O(nu) O(n2) Space? O(m+n)

2 # edges = sum of # neighbors 2m = Σ u in V nu Rest of the graph Give 2 pennies to each edge Total # of pennies = 2m nv=3 u nu=4 v Each edges gives one penny to its end points # of pennies u receives = nu

Questions?

Today’s agenda Run-time analysis of BFS

Breadth First Search (BFS) Build layers of vertices connected to s L0 = {s} Assume L0,..,Lj have been constructed Lj+1 set of vertices not chosen yet but are connected to Lj Use CC[v] array Stop when new layer is empty Use linked lists

An illustration 1 2 3 4 5 7 8 6 1 7 2 3 8 4 5 6

Implementing DFS in O(m+n) time Same as BFS except stack instead of a queue

A DFS run using an explicit stack 7 8 1 7 7 6 3 2 3 5 8 4 4 5 5 3 6 2 3 1

Reading Assignment Sec 3.3, 3.4 and 3.5 of [KT]

Directed graphs Model asymmetric relationships Precedence relationships u needs to be done before v means (u,v) edge

Directed graphs Adjacency matrix is not symmetric Each vertex has two lists in Adj. list rep.

Directed Acyclic Graph (DAG) No directed cycles Precedence relationships are consistent

Topological Sorting of a DAG Order the vertices so that all edges go “forward”