Download presentation

Presentation is loading. Please wait.

Published byDaniella Summers Modified over 3 years ago

1
Graph Searching CSE 373 Data Structures Lecture 20

2
3/7/03Graph Searching - Lecture 202 Readings Reading ›Sections 9.5 and 9.6

3
3/7/03Graph Searching - Lecture 203 Graph Searching Find Properties of Graphs ›Spanning trees ›Connected components ›Bipartite structure ›Biconnected components Applications ›Finding the web graph – used by Google and others ›Garbage collection – used in Java run time system ›Alternating paths for matching

4
3/7/03Graph Searching - Lecture 204 Graph Searching Methodology Breadth-First Search (BFS) Breadth-First Search (BFS) ›Use a queue to explore neighbors of source vertex, then neighbors of neighbors etc. ›All nodes at a given distance (in number of edges) are explored before we go further

5
3/7/03Graph Searching - Lecture 205 Graph Searching Methodology Depth-First Search (DFS) Depth-First Search (DFS) ›Searches down one path as deep as possible ›When no nodes available, it backtracks ›When backtracking, it explores side-paths that were not taken ›Uses a stack (instead of a queue in BFS) ›Allows an easy recursive implementation

6
3/7/03Graph Searching - Lecture 206 Depth First Search Algorithm Recursive marking algorithm Initially every vertex is unmarked DFS(i: vertex) mark i; for each j adjacent to i do if j is unmarked then DFS(j) end{DFS} Marks all vertices reachable from i

7
3/7/03Graph Searching - Lecture 207 DFS Application: Spanning Tree Given a (undirected) graph G(V,E) a spanning tree of G is a graph G’(V’,E’) ›V’ = V, the tree touches all vertices (spans) the graph ›E’ is a subset of E such G’ is connected and there is no cycle in G’ ›A graph is connected if given any two vertices u and v, there is a path from u to v

8
3/7/03Graph Searching - Lecture 208 Example of DFS: Graph connectivity and spanning tree 1 2 7 5 4 6 3 DFS(1)

9
3/7/03Graph Searching - Lecture 209 Example Step 2 1 2 7 5 4 6 3 DFS(1) DFS(2) Red links will define the spanning tree if the graph is connected

10
3/7/03Graph Searching - Lecture 2010 Example Step 5 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4) DFS(5)

11
3/7/03Graph Searching - Lecture 2011 Example Steps 6 and 7 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4) DFS(5) DFS(3) DFS(7)

12
3/7/03Graph Searching - Lecture 2012 Example Steps 8 and 9 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4) DFS(5) DFS(7)

13
3/7/03Graph Searching - Lecture 2013 Example Step 10 (backtrack) 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4) DFS(5)

14
3/7/03Graph Searching - Lecture 2014 Example Step 12 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4) DFS(6)

15
3/7/03Graph Searching - Lecture 2015 Example Step 13 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4) DFS(6)

16
3/7/03Graph Searching - Lecture 2016 Example Step 14 1 2 7 5 4 6 3 DFS(1) DFS(2) DFS(3) DFS(4)

17
3/7/03Graph Searching - Lecture 2017 Example Step 17 1 2 7 5 4 6 3 DFS(1) All nodes are marked so graph is connected; red links define a spanning tree

18
3/7/03Graph Searching - Lecture 2018 Adjacency List Implementation Adjacency lists 12345671234567 246 317 45 561 374 3 14 52 1 2 7 5 4 6 3 G 0 0 0 0 0 0 0 M Index next

19
3/7/03Graph Searching - Lecture 2019 Connected Components 1 2 3 9 8 6 10 4 5 7 11 3 connected components

20
3/7/03Graph Searching - Lecture 2020 Connected Components 1 2 3 9 8 6 10 4 5 7 11 3 connected components are labeled

21
3/7/03Graph Searching - Lecture 2021 Depth-first Search for Labeling Connected components Main { i : integer for i = 1 to n do M[i] := 0; label := 1; for i = 1 to n do if M[i] = 0 then DFS(G,M,i,label); label := label + 1; } DFS(G[]: node ptr array, M[]: int array, i,label: int) { v : node pointer; M[i] := label; v := G[i]; while v null do if M[v.index] = 0 then DFS(G,M,v.index,label); v := v.next; }

22
3/7/03Graph Searching - Lecture 2022 Performance DFS n vertices and m edges Storage complexity O(n + m) Time complexity O(n + m) Linear Time!

23
3/7/03Graph Searching - Lecture 2023 Breadth-First Search BFS Initialize Q to be empty; Enqueue(Q,1) and mark 1; while Q is not empty do i := Dequeue(Q); for each j adjacent to i do if j is not marked then Enqueue(Q,j) and mark j; end{BFS}

24
3/7/03Graph Searching - Lecture 2024 Can do Connectivity using BFS Uses a queue to order search Queue = 1 1 2 7 5 4 6 3

25
3/7/03Graph Searching - Lecture 2025 Beginning of example 1 2 7 5 4 6 3 Queue = 2,4,6 Mark while on queue to avoid putting in queue more than once

26
3/7/03Graph Searching - Lecture 2026 Depth-First vs Breadth-First Depth-First ›Stack or recursion ›Many applications Breadth-First ›Queue (recursion no help) ›Can be used to find shortest paths from the start vertex ›Can be used to find short alternating paths for matching

27
3/7/03Graph Searching - Lecture 2027 Minimum Spanning Tree Edges are weighted: find minimum cost spanning tree Applications ›Find cheapest way to wire your house ›Find minimum cost to wire a message on the Internet

Similar presentations

OK

Search Related Algorithms. Graph Code Adjacency List Representation:

Search Related Algorithms. Graph Code Adjacency List Representation:

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on layer 3 switching Ppt on pi in maths what does median Ppt on range of motion Microsoft office ppt online templates Ppt on earth dam failure Ppt on physical change and chemical change Ppt on central limit theorem statistics Ppt on 4-stroke petrol engine parts Ppt on water resources of maharashtra Ppt on working of nuclear power plant in india