Lecture Notes for CSCI 6966

Lecture 1: August 30

Scope of the course
Project details
The art gallery theorem

Links:

Thierry Dagnino's Art gallery Page

Furher reading:

O'Rourke, J. Art Gallery Theorems and Algorithms. New York: Oxford University Press, 1987.
Urrutia, J. "Art Gallery and Illumination Problems." Ch. 22 in Handbook of Computational Geometry (Ed. J.-R. Sack and J. Urrutia). Amsterdam, Netherlands: North-Holland, pp. 973-1027, 2000.

Lecture 2: September 2

Brief discussion on variants of the Art Gallery Theorem (e.g. 3D)
Complexity classes P and NP
Optimization version of the Art Gallery problem and its hardness
Set Cover problem and the greedy algorithm

Books:

Lecture 3: September 6

LP based approximation algorithms: relaxations, rounding
Randomized rounding applied to set-cover

Links:

Scribe notes from Christos Papadimitriou's class.

Lecture 4: September 9

Geometric instances of the hitting set problem: hitting line segments, placing guards on a circle, ...
Sampling and VC-dimension. In the upcoming lectures, we will follow lectures 19--21 from J. Kleinberg's course

Lecture 5: September 13

The epsilon net theorem. Lecture 20 from J. Kleinberg's course

Lecture 6: September 16

Computing small hitting sets for bounded VC-dimension set systems:

Lecture 7: September 20

An FPTAS for knapsack (chapter 8 from Vazirani)
A PTAS for covering points with uniform disks: Approximation schemes for covering and packing problems in image processing and VLSI

Lecture 8: September 23

Uncertainty representations for triangulation based position estimation (From Alonzo Kelly's lecture notes . The section on position estimation). You may also want to check out this paper.
An algorithm to place cameras to reduce uncertainty in a workspace

Lecture 9: September 27

Voronoi Diagrams and Delaunay Triangulations. Their applications in sensor networks: such as computing (approximate) min. steiner trees, coverage control and maximal breach paths

Lecture 10: September 30

We discussed two papers on the sensor selection problem [paper 1] [paper 2]

Lecture 11: October 4

Introduction to Game Theory. There are excellent resources on the web; The overview in the first part of the course is based on these lecture notes.

October 7-28: Project background, related work and formulation presentations

Lecture 12: November 1

Pursuit-evasion games on graphs. An overview of the cops and robbers game and the role of visibility. We studied the case with 0 visibility and infinite visibility.

Lecture 13: November 4

(cont from last lecture). 1 visibility and i-visibility.

Papers related to Lectures 12 and 13:

Infinite visibility. You can start from this link: Related papers:
Richard Nowakawski and Peter Winkler, Vertex-to-vertex pursuit in a graph, Discrete Math 43 (1983), 235-239.
Graham Brightwell and Peter Winkler, Gibbs measures and dismantlable graphs, J. Comb. Theory (Series B) 78 (2000), pp. 141-169
Zero visibility:
Randomized Pursuit-Evasion in Graphs by M. Adler, H. Racke, C. Sohler, N. Sivadasan and B. Vocking
i-visibility:
V. Isler, S. Kannan, and S. Khanna. Randomized Pursuit-Evasion with Local Visibility.

Lecture 14: November 8

Pursuit-evasion in geometric environments: (Extremely brief!) overview of differential games. The lion and man problem and its variants. Visibility based pursuit-evasion:

Lecture 15: November 11

Online algorithms.

Ski-rental problem
Lost cow problem
The k-server problem: greedy algorithm, lower bound.
(Overview of) Exploration as an online problem: rectilinear polygons, general but simply connected polygons, multiply connected polygons

Last modified: Nov 06 2005