1 / 12

Viceroy: Scalable and Dynamic Emulation of the Butterfly Topology

Viceroy is an overlay routing network with logarithmic path lengths, constant join/leave cost, and balanced congestion. It features a unique topology where each node has specific links and levels for efficient routing. Learn about its distributed level selection, lookup process, congestion analysis, and improvements. Explore the bucket mechanism for maintaining network stability and fault tolerance.

albertdeleon
Download Presentation

Viceroy: Scalable and Dynamic Emulation of the Butterfly Topology

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Viceroy: A scalable and dynamic emulation of the Butterfly Presented in CS294-4 by Sailesh Krishnamurthy Sep 22, 2003

  2. Viceroy • Goals: An overlay routing network with • Logarithmic path lengths • Constant join/leave cost • Balanced congestion (~ log(n)/n) • Keys, servers mapped to unit ring [0,1) • In Chord: each node has all log(n) links • In Viceroy: • Each node has one log(n) link • A link to 1/2k distance points to a node with a link to 1/2(k+1)distance

  3. Viceroy Topology • Each node has a level between 1..log(n) • A `level-k’ node has • “right child”: A long-range link to distance 1/2k (approx.), to a level-(k+1)’ node • “left child”: A local link to `level-(k+1)’ node • Level ring links (pred,succ of the same level) • “up”: A local link to ‘level-(k-1)’ node • Ring links (pred,succ on the ring)

  4. y 0 x 1 Level 1 Level 2 Level 3 Viceroy Topology

  5. Distributed level selection • Select Level (s) • Let n0 = 1/d(s,succ(s)) • Select a level among [1 … log(n0)] uniformly at random • Sanity • When n servers present, then w.h.p. every server estimates: log(n/2logn)<=log(n0)<=3logn • Any level l <log(n/2logn) is “sane”

  6. Lookup target in Viceroy • Three phases: • Proceed to root: up-links to a `level-1’ node • for level k = 1..log(n) • If distance < 1/2k use down-left (short link) • If distance >= 1/2k use down-right (long link) • If reqd down link doesn’t exist (or if you overshoot target) break to next phase • Traverse the ring (pred/succ links, whichever is closer)

  7. Analysis • Constant out-degree • Expected constant in-degree • log(n ) w.h.p. • O(log(n )) lookup steps w.h.p • log(n ) to `level-1’ node • log(n ) for binary search • log(n ) for final local search • Congestion: • Expected log(n )/n lookup load • O(log2(n )/n) w.h.p.

  8. Improving Lookup • Simple lookup - third phase may be too long • May be log2n links to traverse :-( • Fancy lookup • Use a combination of global and level rings to get a dilation of log(n) w.h.p. • Greedy approach - use the level links if you are still too far away from the target.

  9. What happens on node leave? • Problem: we have constant out-degree, but even with a sparse network we could have log(n) in-degree on average • Solution: “buckets” - extra background process • Idea: improve identity/level-selection so that we have constant number of nodes in each stretch of (log(n)/n) nodes • Maintain ~n buckets of ~log(n) contiguous non-overlapping nodes.

  10. Bucket properties • Size: always θ(log(n)) • Merge with neighbouring bucket when size falls below log(n) • Split bucket when size grows above clog(n) • Diversity in bucket • Each level in [1..log(n)] is represented by (1,c) nodes. Claim: this limits the indegree to 2c - how ?

  11. Some comparisons SkipNets log(n) log(n) ?? SkipList

  12. Some questions • How important are const degree networks ? • Dilation and congestion same as chord • Depends on bucket mechanism • What about fault tolerance ?

More Related