IMPORTANT: keep checking the newsgroup of the class and this web page

that we are reading right now if possible all the time and during the last weekend

before the exam, since these are the only ways I can provide

explanations and advice to make your life easier. I intedn to release some sample

questions Friday or Saturday.

__NOTE: __You are allowed to have a one-page (two sides) normal
paper**where you can write whatever you want to remember for the final
exam.**

In addition, as we have already seen, I try to focus on problem-solving

questions instead of "by-heart" recitals. Of course, having read the
material

we have discussed in class and the material from the book will help
you

know the concepts and solcing methods. The midterm and the assignments
are indicative

questions. Variations of the questions nd problems we have seen in
the

midterm, assignments or in the class could be potentail questions.

From the book: Introduction to Algorithms by Cormen et al

Whatever has been discussed in the class is "fair game", the list below

is to help you study and mainly indicate some of the thnigs we have
not

talked about.

You have to be familiar with misc things such as simple proving techniques

(induction), big-O notation, relationships, logarithms, graph
definitions (ch. 5.4, 5.5).

The. = Theorem, Co. = Corollary, Le. = Lemma.

"Except proof of" means except the proof, while you should read
and understand

the theorem.

Ch.23: 23.1 Elementary Graph Algorithms

23.2 Breadth First Search except proof of The. 23.4

23.3 Depth First Search except The. 23.6, Co. 23.7

23.4 except proof of The. 23.11

23.5 Strongly Connected Comp. only the algorithm

Ch. 24: Minimum Spanning Trees

24.1 Generic greedy

24.2 Prim and Kruskal's algorithms

Ch. 25: Single Source Shortest Path Algorithms

25.1 Lemma 25.1, Co. 25.2, Le. 25.3, Relaxation, Le .25.4,
25.5

25.2 Dijkstra (NOT the proof of correctness or the modified DIjkstra complexity

we are happy with the compleity O(V^2))

25.3 Bellman-Ford, Lemma 25.12 (NOT THe 25.- correctness)

Ch. 26: All Pairs Shortest Paths

26.2 Floy-Warshall

Ch. 27: Maximum Flow

27.1

27.2 Ford-Fulkerson (see my explanation page on the web)

Le 27.2, 27.3, Co 27.4, Le 27.5, CO 27.6, The 27.7

(NOT Le 27.8)

27.3 Bipartite Matching Le 27.10 (NOT the proof), 27.11, 27.12

Ch. 36: NP-Completeness

(you are advised to study the notes from the class, and then browse through
the book,

since the book has more stuff)

36.1 Polynomial time.

NOT: the formal language framework (we did not talk about languages and
you are

not expected to know that approach, which is basically an equivalent framework
to what we have been saying)

NOT Lemma 36.1 and Le 36.2

36.2 Polunomial time verification

NOT: the co-P or co-NP classes.

36.3 NP-completeness and reducibility

Fig. 36.5 is important.

THe 36.4 NOT the proof.

NOT the circuit satisfiability.

Steiner tree problem: (see my web-page for s write-up)

Some sample questions:

* execute an alorithm on a small graph (Dijjkstra,
transitive closure, Steiner tree approximation)

* A problem in P is also in NP (yes)

Is it in NP-Complete (no,
NPC intersection P = null according to most scientists)

* Do reduction (transformation) between problem
A to problem B. Is the reduciton polunomial?

* Calculate the competitive ratio of an approximation
algorithm say for the Naive algorith ( Steiner tree)

(see web-page)

etc