Lecture16

# Lecture16 - IE 495 Lecture 16 Reading for This Lecture...

This preview shows pages 1–7. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IE 495 Lecture 16 October 24, 2000 Reading for This Lecture Primary Â¡ Horowitz and Sahni, Chapter 4 Â¡ Kozen, Lecture 3 Secondary Â¡ Miller and Boxer, Chapter 12 (up to page 286) Prim's Algorithm S is the set of nodes in the tree S = {0} for (i = 0; i < n; i++){ SELECT i âˆ‰ S nearest to S; S = UNION(S, i); } Kruskal's Algorithm T is the set of edges in the tree T = for (i = 0; i < m; i++){ SELECT the cheapest edge e if (feasible(UNION(T, e)){ UNION(T, e); } The Red and Blue Rules Start with all edges uncolored The Blue Rule: Â¡ Find a cut with no BLUE edges. Â¡ Pick an edge of minimum weight in the cut and color it BLUE . The Red Rule: Â¡ Find a cycle containing no RED edges. Â¡ Pick an uncolored edge of maximum weight and color it RED . Arbitrary application of the Red and Blue rules will result in a minimum spanning tree (blue edges). Matroids A matroid is a pair (S, I ) where S is a finite set and I is a family of subsets of S such that (i) If J âˆˆ I and I âŠ† J , then I âˆˆ I (ii) If I, J and | I | < | J | , then there exists and x âˆˆ J Â¡ I such that I...
View Full Document

## This note was uploaded on 08/06/2008 for the course IE 495 taught by Professor Linderoth during the Fall '08 term at Lehigh University .

### Page1 / 18

Lecture16 - IE 495 Lecture 16 Reading for This Lecture...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online