Welcome! Cinda Heeren Lecturer Department of CS UIUC The Beauty of Computer Science

Let’s play! 1. People on adjacent vertices must hold different poses. 2. Use the smallest # of poses possible. 3. I specify some poses.

Graph Coloring

Suppose you have 16 friends each of whose talkitivity rating is O, L, P, S, 4 friends per type. No one sitting at the same table can have the same talkitivity rating. No one sitting on the same side of a pair of tables can have the same talkitivity rating. No one sitting in the same “column” can have the same talkitivity rating. Lunchroom Politics Can you seat your friends?

Suppose you have 16 friends each of whose talkitivity rating is O, L, P, S, 4 friends per type. Lunchroom Politics Can you seat your friends? No one sitting at the same table can have the same talkitivity rating. No one sitting on the same side of a pair of tables can have the same talkitivity rating. No one sitting in the same “column” can have the same talkitivity rating.

Lunchroom Politics Can you solve the puzzle? Fill in the grid so that each row, column, and bold 2x2 square has exactly one of each of the digits 1 through 4.

Sudoku Can you solve the puzzle? Fill in the grid so that each row, column, and bold 2x2 square has exactly one of each of the digits 1 through

Sudoku?

I can use my Graph Colorer to solve my Sudoku puzzles! To do so, I just have to run out to the store and buy an adapter that changes my Sudoku puzzle into the right graph…

You can think of the “adapter” and the “graph colorer” as pieces of software. They are programs whose inputs and outputs are well defined. What does this have to do with computer science? Sudoku / Graph Color ADAPTER Beautiful Ultimate Graph Colorer Map Color / Graph Color ADAPTER Exam Scheduler / Graph Color ADAPTER

CS173 Graphs Suppose YOU are the person in charge of scheduling finals. Conflict exams are not allowed…that is, no student can have two exams scheduled for any one time. How many exam periods do you need? Suppose I give you a graph consisting of vertices and edges. Your task is to label the vertices with colors. Vertices which share an edge cannot be colored the same. How many colors do you need? Why are these two problems on the same slide?

CS173 Graphs Graphs are a very general way of representing data. We can use graphs to model things as diverse as: Scheduling problems Routes for travelling between cities Connections between atoms in a molecule Paths that messages can take in a network Dependence relations between events in a large project

CS173 Graphs

Definitions you should understand: Simple Vertex Edge Weights Degree Neighbors Connected Complete Bipartite Planar Cycle Tree Path Circuit

CS 173 Announcements Homework #13 available, due 5/7, 8a. Final exam 5/10, 7-10p, 1404 Siebel, cinda w conflicts. Exam review: 5/9, 5-6:30p, location TBA Section this week is review.