lec7 - CS 323/700 Lecture 7 Design and Analysis of...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
n CS 323/700 ± ± Lecture 7 o Design and Analysis of Algorithms Hoeteck Wee · [email protected] http://algorithms.qwriting.org/
Background image of page 1

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

View Full Document Right Arrow Icon
Spanning trees DEFINITION. spanning tree I input: weighted, undirected, connected graph I spanning tree: subset of edges that forms a tree and every pair of vertices is connected I cost(spanning tree) = sum of edge weights a b c d e f g 7 8 5 9 7 5 15 6 8 9 11 PROBLEM. minimum spanning tree (MST) problem I find a spanning tree of the smallest cost I non-trivial: complete graph Kn has ( n - 1 )! = n Ω( n ) spanning trees. I see two greedy algorithms for MST Hoeteck Wee CS 323/700 Feb 24, 2010 2 / 12
Background image of page 2
Minimum spanning tree APPLICATION. I input: a set of locations V = { v 1 , . . . , vn } , with costs for building a (undirected) link between some pairs of locations I goal: build the cheapest communication network s.t. every pair of locations is connected (cost of a network = sum of link costs) a b c d e f g 7 8 5 9 7 5 15 6 8 9 11 FACTS. I cheapest communication network must be a spanning tree (removing any edge from a cycle in a connected graph leaves the graph connected) I every n -node tree has exactly n - 1 edges Hoeteck Wee CS 323/700 Feb 24, 2010 3 / 12
Background image of page 3

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

View Full Document Right Arrow Icon
Kruskal’s MST algorithm ALGORITHM. incrementally add least cost edges that do not make a cycle sort edges by cost, T = [] for e in edges: if adding e to T does not create a cycle: T.append(e) return
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 12

lec7 - CS 323/700 Lecture 7 Design and Analysis of...

This preview shows document pages 1 - 5. Sign up to view the full document.

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