Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this presentation? Why not share!

- GoFFish - A Sub-graph centric frame... by charithwiki 1912 views
- Three-dimensional video by Marco Cagnazzo 2242 views
- VENUS: Vertex-Centric Streamlined G... by Qin Liu 896 views
- The Innovative Service Platform for... by Hatio, Lab. 3288 views
- Unbounded bounded-data-strangeloop-... by Monal Daxini 1120 views
- Dongwon Kim – A Comparative Perform... by Flink Forward 10900 views

1,274 views

Published on

Published in:
Education

No Downloads

Total views

1,274

On SlideShare

0

From Embeds

0

Number of Embeds

543

Shares

0

Downloads

10

Comments

0

Likes

1

No embeds

No notes for slide

Re-cap : At each iteration

- 1. *
- 2. * *Vertex centric SSSP *Sub-graph Centric SSSP *Performance improvements
- 3. * A C D B F G E H1 1 4 3 1 2 2 2 1 2 1 Source : A A B C D E F G H 0 INF INF INF INF INF INF INF 0 3 1 4 INF INF INF INF 0 3 1 2 4 3 INF INF 0 3 1 2 4 3 5 5 1 Assume no –ve edges
- 4. s d v At each superstep… … vertex receives messages which contain the current known shortest path through a neighbor d0 d1 d s d t ws wt if min(d0,d1) < dv, it sends messages to its neighbors and updates its new minimum distance from s else, it votes to halt d0 + ws d0 + wt After execution, each vertex’s value is its minimum distance from s
- 5. * *Computation time bounded by number of super steps take for computation * super step time * After ith super-step all vertices whose shortest path consist of i-1 number of edges will get the final value. *Let d be the longest shortest path in the graph (assume unit edge weights) *Number of super-steps = O(d) A C D B F G E H1 1 4 3 1 2 2 2 1 2 1
- 6. * *Partition graph into set of connected components – sub-graphs *Terms : *Sub-graph : Partition *Remote vertex : Let v in SGj and let edge (u,v) s.t. v in SGi. Then for SGi vertex v is a remote vertex. *Remote edge : (u,v) s.t. u in SGi v in SGj and SGi≠ SGj SG1 SG2 SG3
- 7. * A C D B F G E H1 1 4 3 1 2 2 2 1 2 1 S Q=V-S Iterative section
- 8. At each super-step… • Each neighbor vertex in sub-graph with incoming edges will receives messages which contain the current known shortest path through a neighbor • Set that value as the vertex value if its less than current value • Add that vertex in open set (V-S) with the new value • Run Iterative section of Dijkstras locally and calculate new Shortest paths. • Sent new shortest path though this sub- graph to its remote vertices d0 d1 d0 d1 Input edge Input edge output edge output edge S V-S
- 9. * *Assume sub-graph is a vertex s d v At each superstep… … • Vertex receives messages which contain the current known shortest path through a neighbor • Vertex sends its current known shortest path through it to its neighbors if they have changed d0 d1 d s d t ws wt d0 + ws d0 + wt
- 10. * d0 d1 Input edge Input edge output edge output edge S V-S • Set incoming values as the vertex value if its less than current value • Add that vertex in open set (V-S) with the new value • Run Iterative section of Dijkstras locally and calculate new Shortest paths (Same as assuming virtual source and running Dijkstras) • Sent new shortest path though this sub- graph to its remote vertices if changed • Vertex receives messages which contain the current known shortest path through a neighbor • Vertex sends its current known shortest path through it to its neighbors if they have changed Virtual source *Assume sub-graph is a vertex
- 11. * *Computation time bounded by number of super steps take for computation * super step time *Super-step time for super step i= O(e*log(v)) (e ,v = edges and vertices of largest updating sub-graph at super-step i) * After ith super-step all sub-graphs whose vertices shortest path consist of i-1 number of remote edges will get the final value. *Let d be the longest shortest path in the graph where sub- graphs are vertices (assuming unit edge weights) *Number of super-steps = O(d)
- 12. * 0 200 400 600 800 1000 1200 1400 RN - CA TR LJ Giraph GoFFish Runtime comparison • RN-CA: Road network • TR : Trace route map • LJ : Live Journal graph
- 13. * *Run time = # super-steps x super-step time *Vertex centric – negligible vertex compute time *Sub-graph centric – sub-graph compute time depend on size of the sub-graph (# edges, # vertices) *Out performs vertex centric for sparse graphs with large diameter

No public clipboards found for this slide

Be the first to comment