Advanced topics in algorithms

Spring 2011/2012, Tel Aviv University

Lecturer: Haim Kaplan
Time: Wednesday, 16-19
Place: Physics 222

Announcements:

·         In response to a few questions we added some more information to the last presentation on planar graphs. In particular we tried to clarify the definition of a leftmost path from s to t  in a general directed planar graph

·         Homework 5 contains 2 problems on planar graphs, just for you to practice, don't hand it in. I added a sketch of the solutions below.

·         Homework 3 and 4  are graded, you can pick it up at my office.

·         Final exam is set to be on Friday July 20 at 9am

·         The exam will take 3 hours. You would have to choose 3 questions out of 5

·         This link contains 3 questions that you could use to prepare for the exam, I corrected a few minor mistakes in question 2 that you pointed out.

Tentative topics:

·         Totally monotone matrices and some applications

·         Splay trees.

·         Dynamic trees

·         Maximum flow

·         Minimum cost flow

·         Finger search trees and their applications

·         Distances in graphs

·         Persistent data structures

 

Presentations

 

·         Totally monotone matrices and the SMAWK algorithm

·         The concave least weight subsequence problem

·         Submatrix maximum queries in Monge matrices

·         Approximate optimal search trees  (Following the class, I prepared an alternative presentation of the same algorithm that does not split the items into two equal halves to begin with, as I did in class. It may be more natural, take a look here)

·         Finger search trees

·         SSSP inside a polygon (This presentation was revised after class to clarify some questions that came up)

·         Splay trees

·         Maximum flow

·         Dynamic trees

·         Minimum cost flow

·         Dynamic spanning forest (planar graphs)

·         Dynamic connectivity (general graphs)

·         Maximum flow in planar graphs

·         More on maximum flow in planar graphs

 

List of homework

 

·         Homework 1 (there were a few minor mistake in q. 4, now corrected.)

·         Homework 2

·         Homework 3

·         Homework 4 (I corrected mistakes in q. 4 and q. 5)

·         Homework 5

 

Selected solutions (by you guys), please use with care, answers often are not perfect but the best we could find

 

·         Homework 1 c.1 c.2

·         Homework 2 c.1 c.2

·         Homework 3 c.1 c.2

·         Homework 4 c.1 c.2

·         Homework 5 (sketch)

 

Bibiliography lists

 

·         Totally monotone matrices and the SMAWK algorithm

·         Finger trees, optimal search trees, splay trees, and maximum flow

·         Minimum cost flow, dynamic connectivity

·         Maximum flow in planar graphs