Download presentation

Presentation is loading. Please wait.

Published byAshley Montgomery Modified over 2 years ago

1
Breadth-First Search and Shortest Path Kevin Schaffer Chapter 15.4 from “Distributed Algorithms” by Nancy A. Lynch

2
Outline Breadth-First Search AsynchBFS LayeredBFS HybridBFS Shortest Path AsynchBellmanFord

3
AsynchBFS Similar to AsynchSpanningTree AsynchSpanningTree algorithm does not always generate a breadth-first spanning tree AsynchBFS detects incorrect parent assignments and corrects them

4
Safety and Liveness Safety For every process i i 0, dist i is the length of some path p from i 0 to i in G in which the predecessor of i is parent i. For every message m in channel C i,j, m is the length of some path p from i 0 to i. Liveness For every pair of neighbors i and j, either dist j dist i + 1, or else either send(j) i or C i,j contains the value dist i.

5
Complexity of AsynchBFS Message complexity: O(n|E|) A node can receive at most n estimates, each of which generates |E| messages Time complexity: O(diam n(l + d)) Length of the shortest path from i 0 to any node is diam and at most n messages are ever in any channel

6
Termination in AsynchBFS Problem with AsynchBFS: Processes do not know when to terminate Solution: Modify algorithm to perform a convergecast/broadcast at the end Not as straight-forward as AsynchBcastAck since processes may participate multiple times

7
LayeredBFS Constructs the BFS tree in phases Each phase adds one layer to the tree; layer k contains the nodes at depth k in the tree Upon completion of phase k, all processes with depth at most k know their parent and those at depth at most k – 1 know their children Acknowledgements let i 0 know when each phase is complete

8
Complexity of LayeredBFS Message complexity: O(|E| + n diam) At most |E| search and acknowledgements At most diam + 1 phases At most n newphase/convergecast messages Time complexity: O(diam 2 (l + d)) Each phase takes diam(l + d)

9
HybridBFS HybridBFS performs an AsynchBFS multiple times, completing m layers during each phase If m = 1 then HybridBFS is similar to LayeredBFS and if m = diam then HybridBFS is similar to AsynchBFS

10
AsynchBellmanFord Generates a shortest path tree rooted at i 0 Similar to AsynchBFS but sends weighted distances Same problem with termination as AsynchBFS

11
Complexity of ABF Worst-case is exponential Message complexity: O(n n |E|) Maximum number of distinct simple paths Time complexity: O(n n + 1 (l + d))

Similar presentations

OK

CPSC 668Set 2: Basic Graph Algorithms1 CPSC 668 Distributed Algorithms and Systems Spring 2008 Prof. Jennifer Welch.

CPSC 668Set 2: Basic Graph Algorithms1 CPSC 668 Distributed Algorithms and Systems Spring 2008 Prof. Jennifer Welch.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on bluetooth protocol architecture Ppt on apple ipad Ppt on inside our earth Ppt on types of business organisations Ppt on leadership quotes Ppt on c language history Ppt on 2 dimensional figures and 3 dimensional slides shoes Ppt on the art of war pdf Ppt on traffic light controller using fpgas Ppt on collections framework in java