Locality Aware Network Solutions

1. Locality Aware Network Solutions Dahlia Malkhi The Hebrew University of Jerusalem

2. A Brief Overview of Distributed Computing • The 90’s: • Internet activity: Web browsing • Paradigm: Client-server • Techniques: cluster computing, Paxos, group communication

3. A Brief Overview of Distributed Computing • 2000- • Internet activity: File sharing • Paradigm: P2P, grid, web-services • Techniques: overlay networks, content distribution networks, resource location • The 90’s:

4. 8888:::0909:9999 567A:::0202:0202 EEE0:::EEEE:EEEE 0001:::3BBB:5555 AF3S:::3FF1:43E4 1111:::7777:7754 2222:::2222:2222 5151:::6161:6666 Application: IPv6 Routing over IPv4[van Renesse 02] Distribute Hash Tables (DHT)

5. Application: Content Delivery / Finding Nearest Copies of Data ? ? ?

6. Key Alice Bob Application: Hyperencryption[Maurer 92, Ding & Rabin 02] Random bits Adversary bits

7. Application: A Hyperencryption P2P Network[Rabin 03] Distributed Hash Table (DHT)

8. Application: A Distributed Google? ?

9. Scalable Network Solutions • Overlay networks provide added functionality at the application level • Search, routing, location services • Network theory provides the foundations • Possibilities, impossibilities, lower/upper bounds • Practical solutions require flexible deployment

10. Distributed Data Structures (DDS) • Peers jointly implement a data structure, e.g., hash table • Route queries based on data-name (key)

11. DDS Problem Reduced to Routing ?? 00001111 Responsible for 00001111

12. Static # of nodes a priori known Node labels designated by network designer Why classic routing network designs don’t help 111 011 101 001 110 010 000 100

13. DDS Reduced to Routing • The problem: Overlay routing network • Variants: labeled routing, name-independent routing, finding nearest copies • Dynamic emulation

14. Distributed Hash Tables [Malkhi, Naor, Ratacjzak, PODC 2002] [Abraham, Awerbuch, Azar, Bartal, Malkhi, Pavlov, IPDPS 2003]

15. Leafs of the tree represent current nodes Inner nodes in the tree represent nodes that were split Tree View of Dynamic Graphs 111 011 101 001 010 110 00 000 100 00 000 001 010 011 100 101 110 111 • Example: merge of 000, 001 into 00

16. source target Locality awareness

17. source target Locality awareness

18. Locality Awareness in Overlay Networks • Model the network as a weighted undirected graph • c(x, y): cost of shortest path from x to y • c() is a metric • An overlay network is a sub-graph • Letx=x0 , x1, …, xt=y be a route in the overlay network • Stretch: Ratio between overlay route cost and shortest path cost:( c(x, x1) + c(x1,x2) + … c(xt-1, y) ) / c(x,y)

19. Overlay Networks inGrowth-Bounded Metrics • Previous work: • [Plaxton, Rajaraman, Rica 1997], Tapestry (Berkeley), Pastry (MS UK) • Expected (large) constant stretch • Logarithmic node degree • LAND[Abraham, Malkhi, Dobzinski, SODA 2004]: • Guaranteed stretch (1+ε) • Expected logarithmic node degree, constant depends on growth-bound • Simple, intuitive construction and proofs

20. Overlay Networks in Geometric Spaces • Modeling the Internet as a geometric space is practical • Ubiquitous GPS devices • Successful embeddings in virtual coordinate-space • Problem 1: Locate nodes • Problem 2: Route to known coordinates

21. Location Services and Routingin Geometric Spaces • LLS: First fully-locality aware location service [Abraham Dolev Malkhi 2004] • bounded stretch lookup • bounded stretch update • First constant-degree routing scheme (to known coordinates)[Abraham Malkhi, PODC 2004] • constant node degree, logarithmic hops, 1+ε stretch

22. Routing in Arbitrary Graphs: Lower and upper bounds • Name-independent routing: node names are independent of routing scheme [Awerbuch, Bar Noy, Linial, Peleg 1989] • Lower bounds: [Gavoille Gengler 2001] • Stretch < 3  O(n) routing information • Stretch < 5  √n routing information • Upper bound: [Abraham, Gavoille, Malkhi, Nisan, Thorup, SPAA 2004] • stretch-3 routing with O(√n ) routing information • Stretch 3 is indeed attainable! • General upper bound: [Abraham Gavoille, Malkhi, DISC 2004] • Stretch-k routing with memory O(k2k√n )

23. EVERGROW ever-growing global scale-free networks, their provisioning, repair and unique functions The Vision ultimate GOOGLE ultimate AKAMAI ultimate GNUTELLA ultimate RAID infrastructure and new methods and systems devoted to measurement, mock-up and and analysis of present and future network traffic, topology and logical structure, to bridge the gap in theory, protocols and understanding to what the Internet can be in 2025. An EC project. Coordinators: SICS (Sweden) and HUJI (Jerusalem)

24. Locality-Aware, Robust Overlay for Information Lookup and Content Delivery • Degree O(√n) • Locality awareness: • Formally stretch 3 • For far-apart nodes, lower stretch • Mostly two-hop • Whenever full connectivity exists • Flexibility • Estimate √n roughly • Cache information on many vicinity nodes • Store information about any known node of same color • Fault tolerance: • Multiple route choices • Quick repair • Maintain QoS in face of churn

25. Thank you!

26. Large Scale Content Delivery • Initially split the content • Then cross-exchange data pieces • Solutions build on top of overlay routing networks

27. FastReplica Cherkasova,Lee -HP Labs - 2003 • Phase 1 Source Clients

28. FastReplica Cherkasova,Lee -HP Labs - 2003 • Phase 2 Source Clients

29. Locality motivation – Tree example

30. Julia algorithm motivation: “Divide and conquer” First phase

31. 2nd phase 2nd phase Julia algorithm motivation: “Divide and conquer”

32. Network nodes

33. Nodes’ random identifiers 1001001 0101001 0111010 0001000 1111110 0011110

34. Coloring and Vicinities

35. Coloring and Vicinities ? ? ? ?

36. Stretch 3 ? d ≤ 2d ≤ d

37. ? 5 b 4 d ? 3 c 2 1 a The Full Routing Scheme