Download presentation

Presentation is loading. Please wait.

Published byDulce Grimes Modified over 3 years ago

1
Compact Routing with Slack in Low Doubling Dimension Goran Konjevod, Andr é a W. Richa, Donglin Xia, Hai Yu CSE Dept., Arizona State University {goran, aricha, dxia}@asu.edu CS Dept., Duke University fishhai@cs.duke.edu

2
Doubling Dimension The least value s.t. any ball can be covered by at most 2 balls with half radius Euclidean plane: = log 7

3
Related Work: Name-independent compact routing schemes ReferenceWith SlackStretchRouting TableHeaders [KRX’07] 9+ [Dinitz’07] slack This paper (1- )n nodes 1+ n nodes This paper (1- )n nodes1+ n nodes9+ Lower Bound [KRX’06]: GraphDoubling DimensionDiameterRouting tableStretch Tree : Doubling Dimension; 1/polylog(n)

4
Overview Basic Idea Slack on Stretch Conclusion

5
Basic Idea Using underlying labeled routing scheme [KRX’07] (1+ ) stretch (log n)-bit label Mapping original names to routing labels Hierarchically storing (name, label) pairs Search procedure to retrieve routing label

6
r-Nets An r-net is a subset Y of node set V s.t. x, y in Y, d(x,y) r u V, x Y s.t. d(u,x) r r-net nodes:

7
Hierarchy of r-nets r-nets: Y i : 2 i -net for i=0, …, log : normalized diameter Zooming Sequence: u(0)=u u(i) is the nearest node in Y i to u(i-1)

8
Ball Packing s-size Ball Packing B Greedily select disjoint balls B u (r u (s)) in an ascending order of their radii r u (s) (where r u (s) is the radius s.t. |B u (r u (s)))|=s ) B j : 2 j -size ball packing, for j=0, …, log n B(u,j) B j : the nearest one to u c(u,j): the center of B(u,j)

9
Counting Lemma D ij : the set of u Y i s.t. c=c(u,j) Counting Lemma

10
Overview Basic Idea Slack on Stretch Conclusion

11
(1+ )-stretch B u(i) (2 i / ) contains info of B u(i) (2 i / 2 ) Not found at u(t-1) Routing Cost:

12
Data Structure (1) A search tree on any B in B j, stores info of B c (r c (2 j g 1 )) where g 1 =log 2 n/( 14 )

13
Data Structure (2) For each u(i) If B in B j s.t. B B u(i) (2 i / ) B u(i) (2 i / 2 ) B c (r c (2 j g 1 )) If not, search tree on B u(i) (2 i / ) stores info of B u(i) (2 i / 3 )\B c (2 i+2 ), if u(i) D ij where c=c(u,j), j=log (|B u (2 i / )|g 2 ), and g 2 =log 2 n/( 10 ) B u(i) (2 i / )

14
Searching at u(i) Go to c, and search on B cost: 2 i+1 / info: B u(i) (2 i / 2 ) next level: i+1 Search on B u(i) (2 i / ); if u(i) D ij, go to c and search on B c (2 i+2 ) cost: 2 i+1 / 2 Info: B u(i) (2 i / 3 ) next level: i+log(1/ )+1

15
Slack on Stretch Counting lemma 9+ Stretch Not at level t-1 cost

16
Conclusion (1+ )-stretch compact name- independent routing schemes with slack either on storage, or on stretch, in networks of low doubling dimension. Dinitz provided 19-stretch -slack compact name-independent routing scheme in general graphs Can we do better than 19 stretch in general graphs?

17
Thanks & Questions

Similar presentations

OK

Oct 23, 2005FOCS 20051 Metric Embeddings with Relaxed Guarantees Alex Slivkins Cornell University Joint work with Ittai Abraham, Yair Bartal, Hubert Chan,

Oct 23, 2005FOCS 20051 Metric Embeddings with Relaxed Guarantees Alex Slivkins Cornell University Joint work with Ittai Abraham, Yair Bartal, Hubert Chan,

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on rabindranath tagore in english Means of communication for kids ppt on batteries Free ppt on moving coil galvanometer principle Ppt on media revolutionary Ppt on content development jobs Ppt on brand marketing agencies Ppt on amplitude shift keying spectrum Ppt on data collection methods statistics Ppt on magic maths Ppt on astronomy and astrophysics courses