Lecture9 - CME 305: Discrete Mathematics and Algorithms...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CME 305: Discrete Mathematics and Algorithms Instructor: Professor Amin Saberi (saberi@stanford.edu) February 2, 2010 Lecture 9: Applications of Network Flow Problem In this lecture, we discuss three problems that can be modeled as network flow problems; (i) baseball elimination, (ii) project scheduling, (iii) airline flight scheduling. Chapter 7 of the textbook (Kleiberg and Tardos [KT]) discusses many other applications of network flow to solve different types of problems. 1 Baseball Elimination Problem: Suppose we are in the middle of a baseball season where each team T i , 1 i n has won W i games so far and thus has W i points (recall that in baseball each game has one point and we cannot have a tie.). Let G 1 ,G 2 ,...,G k be the schedule of the remaining games, where each G i is an unordered pair of teams. Question: Given T i , W i , 1 i n , and G 1 ,G 2 ,...,G k , can we predict that T 1 does or not does not have a chance to have the top score at the end of the season? if T 1 has a chance of being champion, how can we find a sequence of outcomes (i.e. results of G 1 ,G 2 ,...,G k ) such that T 1 reaches the top rank at the end of the season? Answer: Let g ( i ) be the number of games that team i will play until the end of the season. Let W * 1 = W 1 + g (1) which is the maximum final score of T 1 . If there exists....
View Full Document

Page1 / 2

Lecture9 - CME 305: Discrete Mathematics and Algorithms...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online