Lecture16

Lecture16 - IE 495 Lecture 16 October 24, 2000 Reading for...

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Unformatted text preview: IE 495 Lecture 16 October 24, 2000 Reading for This Lecture Primary Horowitz and Sahni, Chapter 4 Kozen, Lecture 3 Secondary 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 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: Find a cut with no BLUE edges. Pick an edge of minimum weight in the cut and color it BLUE . The Red Rule: Find a cycle containing no RED edges. 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 I and I J , then I I (ii) If I, J and | I | < | J | , then there exists and x J I such that I...
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Lecture16 - IE 495 Lecture 16 October 24, 2000 Reading for...

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