1 / 15

Dynamic Load Balancing in Distributed Hash Tables

Dynamic Load Balancing in Distributed Hash Tables. Marcin Bieńkowski Mirosław Korzeniowski Friedhelm Meyer auf der Heide. Ring / Hypercube Topologies. .1. Chord, Tapestry, Pastry, de Bruijn Space: ring [0,1] Arithmetics mod 1 Links to: predecessor and successor shortcuts Degree: log n

leanne
Télécharger la présentation

Dynamic Load Balancing in Distributed Hash Tables

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. Dynamic Load Balancing in Distributed Hash Tables Marcin Bieńkowski Mirosław Korzeniowski Friedhelm Meyer auf der Heide

  2. Ring / Hypercube Topologies .1 • Chord, Tapestry, Pastry, de Bruijn • Space: ring [0,1] • Arithmetics mod 1 • Links to: • predecessor and successor • shortcuts • Degree: log n • Diameter: log n (or log n / log log n) • Balance: (log n) • Smoothness (ratio of the longest and shortest interval): (n¢log n) .12 .2 .23 .25 .3 .32 .5 .4 .45 Server Key

  3. Balls into Bins If we throw n balls into n bins uniformly at random, the fullest bin will have (log n / log log n) balls. If we throw n¢log n balls into n bins, each bin will have (log n) balls If we throw n balls sequentially into n bins and each ball chooses the emptiest of log n randomly chosen bins, each bin will have (1) balls

  4. Previous Results Recent publications concerning balancing in P2P: • Moni Naor, Udi Wieder „Novel Architectures for P2P Applications: the Continous-Discrete Approach” SPAA 2003 • Micah Adler, Eran Halperin, Richard Karp, Vijay Vazirani „A stochastic process on the hypercube with appications to peer-to-peer networks” STOC 2003 • Both optimal  • Both sequential 

  5. Previous Results Recent publications concerning balancing in P2P: • David Karger, Matthias Ruhl, Simple Efficient Load Balancing Algorithms for Peer-to-Peer Systems, SPAA 2004 • each join / leave operation makes log log n nodes migrate • Gurmeet Singh Manku, Balanced Binary Trees for ID Management and Load Balance in Distributed Hash Tables, PODC 2004 • a general algorithm, needs locally centralized decisions

  6. Assumptions • We know: • n (the number of nodes) def.  := 1/n • or at least log n • or at least an upper bound on log n • No interaction during rebalancing • Any initial state of the network • The network organises itself and implements: • join(where) • leave • insert(hash)

  7. Lazy nodes leave First phase: if (length < 1/10¢) leave Minimizing balance = minimizing smoothness Balance = the longest interval Smoothness = ratio between the longest and the shortest interval

  8. Continous scheme All the next phases: if (length < 4¢) eitherpropose(random) or not if (length > 10¢) halve using the first proposal elseforward (log n) times Analysis (sketch) • There are (n) proposals • Interval longer than (¢log n) receives enough proposals in one step (w.h.p.) • Interval shorter than (¢log n) receives enough proposals from its predecessors

  9. To Propose or Not to Propose Many consecutive short intervals: L R L R L R L R L R L R L R L L R L L R R R L L R L L L

  10. Continous scheme All the next phases: if (length < 4¢) eitherpropose(random) or not if (length > 10¢) accept(length / 10) if (length < 10¢) forward(log n) Analysis (sketch) • There are (n) proposals • Interval longer than (¢log n) receives enough proposals in one step (w.h.p.) • Interval shorter than (¢log n) receives enough proposals from its predecessors

  11. Managing the volunteers – 1st phase

  12. Managing the volunteers – 2nd phase

  13. Estimating n and  • Choose global k >  (log n) • Each node inserts k markers into the network • (n¢log n) markers are distributed uniformly • An interval of length  contains (k) items w.h.p. • Instead of lengths we consider the number of markers (weights) • If a node should insert a normal item it replaces a marker with it ) load increased only if it was low

  14. Results • A scheme that • copes with insertions and deletions • works in constant number of rounds • each round takes logarithmic time • has optimal number of migrations(up to a constant factor) • each node migrates at most once • has bounded communication per half-life

  15. Dynamic Load Balancing in Distributed Hash Tables Thank you for your attention

More Related