LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment W. LITWIN CERIA Laboratory H.YAKOUBEN Paris Dauphine University Paris Dauphine University T. SCHWARZ Santa Clara University (USA)

LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment 2 Plan  Objective  Overview: SDDS & P2P  LH* RS P2P  Architecture  Addressing  Properties  Churn Management  Conclusion

Design a new SDDS for a structured P2P environment A High available Data Structure and treatment of CHURN LH*RS P2P key search requires at most one forwarding message LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment 3 Objective High availability to deal with churn At most one forwarding message for key search or insert or scan (fastest known performance) Very Large Scalable Files

A File of records identified by keys SDDS client nodes face the applications and send queries to SDDS server nodes No centralized addressing Servers contain application or parity data  In buckets Overflowing servers split on new servers Servers do not notify clients about splits SDDS (1993) LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment 4

Clients use images of the file state for addressing  Key based  Range queries  Scans  … Images get adjusted towards the file state during queries by Image Adjustment Messages  Triggered by incorrect addressing by the client IAMs reflect the file evolution by splits or, rarely, merges. IAMs reflect also the location changes because of failures and recovery SDDS (1993) 5 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment

6 SDDS Typology LH* sa SDDS(1993) Data Structures Classics Tree m-d Tree 1-d Tree RP*, k-RP*, SD-Rtree, DRT*, LH*, DDH, EH*, Hash High Availability 1-dimensional d-dimensional IH*… LH* rs LH*s Alg. Sign… k-Availability Security LH* m LH* g LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Structured P2P Schemes CHORD... BATON VBI-Tree

New Peer 7 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Clients Growth through splits under inserts Peer SDDS Expansion

8 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Clients SDDS Client Image Evolution Image Adjustment Messaging

Available at CERIA site Announced at DbWorld Managing LH* RS and RP* files  In distributed RAM  Uner Windows  Over 1gbs Ethernet Various functions  Response time reaching 30 microsec  Up to 300 times faster than disk files SDDS 2007 Prototype 9

Autonomous nodes store and search data By flooding in early systems  Freenet, Napster, Gnutella… Structured P2P reduce the flooding  Using decentralized data structures Distributed Hash Table (DHT) especially  Few folks know the concept is due to B. Devine  FODO 93  Chord, P-tree, VBI, Baton… Structured P2P schemes are specific SDDS schemes P2P (1995 ?) 10

11 Client Address Calculus a’  h i’ (C ) ; /* a’ is the address of peer destination of the key C*/ if a’ < n’ then a  h i’+1 (C ) ; LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Global Addressing Rule a  h i (C ) ; /* a is the address of peer destination of the key C*/ if a < n then a  h i+1 (C ) ; /* (i, n) state of an SDDS file, they are only known to the file coordinator node LH* RS P2P Addressing h i (C ) = C mod 2 i

File starts with i = 0 and n = 0 and a single data bucket 0 Every bucket m keeps the bucket level j of hash function h i last used to split, j = 0 initially. Overflowing bucket m alerts the coordinator Coordinator notifies bucket n to split Bucket n applies h i + 1 About half of keys migrates to new bucket n + 2 i Bucket n and the new one set j = j + 1 Coordinator performs  n = n + 1  if n = 2 i then i = i + 1 and n = 0 LH* RS P2P File Expansion 12

Architecture based on LH* RS 13 LH* RS P2P j i’ n’ Client Part Server Part LH* P2P Peer LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment LH* RS P2P Peer LH* RS Client LH* RS DB Candidate Peer Client & Spare Storage LH* RS P2P Peer LH* RS Client LH* RS PB Pupils

14 i’ = j-1 ; /* j value before the split n‘ = a +1 /* a is the splitting bucket if n’ = 2 i’ then i’ = j + 1 ; n’ = 0 ; LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer & Pupil Image Adjustment During Peer Split

15 Before splitting Coordinator Peer (CP) P0 j=2 i’=1 n’=1 P2 P1 i=1 n=1 j=1 i’=1 n’=0 j=2 i’=1 n’=1 After splitting j=2 i’=2 n’=0 CP P0 j=2 i’=1 n’=1 P2 P1 i=2 n=0 j=2 i’=2 n’=0 j=2 i’=1 n’=1 P3 i’= j =1; n’= m+1= 1+1; If n’=2 1 then n’=0; i’= i’+1 and (i’, n’)= (2,0) LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Example

16 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Server Address Calculus a’  h j (C ) ; if a’= a then exit/* Bucket a is the correct one else send C to bucket a /* Forwarding to bucket a’ exit;  Simpler and faster than for LH*  As only one forwarding is possible

17 i’  j - 1, n’  a + 1 ; if n’ >2 i’ then n’  0 ; i’  i’ + 1 ; LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer Image Adjustment by IAM  IAM comes from the correct bucket  Bucket a is the forwarding one  Bucket level j is that of the correct bucket  0f the forwarding one as well Same algorithm as for the adjustment of the local client and of pupils after a split

18 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment PC i =3 n=2 P0 j=4 i’=3 n’=1 Pairs P4 j=3 i’=2 n’=1 P9 j=4 i’=3 n’=2 P1 j=4 i’=3 n’=2 9 9 Checking and forward the key using A2 Peer Image Adjustment by IAM IAM a = 1 j = 4

19 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment PC i =3 n=2 P0 j=4 i’=3 n’=1 Pairs P4 j=3 i’= 3 n’= 2 P9 j=4 i’=3 n’=2 P1 j=4 i’=3 n’=2 9 9 Peer Image Adjustment by IAM IAM a = 1 j = 4

20 Example of the File Expansion PC i=2 n=2 P0 j=3 i’=2 n’=1 Peers P2 j=2 i’=1 n’=1 P5 j=3 i’=2 n’=2 Candidate Peer i’=0 n’=0 P6 j=3 i’=2 n’=3 i=2 n=3 i’=2 n’=3 j=3 Pupil i’=2 n’=1 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Assign a Tutor for Candidate Peer: LH-hash of the client IP Address TUTOR, Update Pupil LH* RS P2P

21 1. The maximal number of forwarding messages for the key search is one. 2. The maximal number of rounds for the scan search can be two. 3. The worst case addressing performance of LH* RS P2P as defined by Property 1 is the fastest possible for any SDDS or a practical structured P2P addressing scheme. LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Properties of LH* RS P2P :

22 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Proof Property 1 nn+2 i’ 2 i’ a’ 0 a  Case 1 : i’ = i and n’ < n  Peer a addresses peer a’, using its image (i’,n’) from last split  No IAM came since. j = i’+1 j = i’ No forwarding a+2 i’

23 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Forwarding possible for any address a’ between (a, n)  Case 1 : i’ = i and n’ < n  Peer a addresses peer a’, using its image (i’,n’) from last split  No IAM came since. nn+2 i’ 2 i’ a’ 0 a j = i’+1 j = i’ a+2 i’ Proof Property 1

24 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Forwarding possible for any address a’ beyond [n, a]  Case 2 : i = i’ + 1 and n < n’  Peer a addresses peer a’, using its image (i’,n’) from last split  No IAM came since. n n+2 i’+1 2 i’ a’ 0 a j = i’+2 j = i’+1 j = i’ 2 i’+1 Proof Property 1

25 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer a sends the scan to all buckets in its image Including its image (i’, n’) Receiving peer a’ can have bucket level j as in the image j (a) = j’ (a) No forwarding of the scan Or, bucket a’ split Once and only once j (a) = j’ (a) + 1 See the figs for the key address calculus Proof Property 2

26 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer a’ forwards the scan to its (only) child No child can have a child Peer a would first need to split again as well Every peer gets thus the scan and only once There at worst two rounds Proof Property 2

27 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment The only faster worst case performance is zero forwarding messages Every split has to be notified then to every peer It would be against the scalability goal of every SDDS & structured P2P scheme Proof Property 2

28 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment LH* RS P2P Churn Management Bucket reliability group with k parity buckets protect against up to k bucket failures per group Parity PeerData PeerRank Parity RecordData Record Tutoring records

29 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer leaves with notice Coordinator Peer j i’,n’ j j j P0P0 PmPm PlPl Candidate Peer Notification … … Say that’s OK LH* RS P2P Churn Management

30 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer leaves without notice or fails Coordinator Peer j i’,n’ j j j P l-1 PmPm PlPl Parity Peer Query Forward LH* RS Bucket Recovery LH* RS P2P Churn Management

31 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Peer leaves without notice or fails Coordinator Peer j i’,n’ j j j P l-1 PmPm PlPl Parity Peer Answer LH* RS Bucket Recovery LH* RS P2P Churn Management

32 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Sure Search : Protects against outdated server read (transient communication or peer failure) Coordinator Peer j i’,n’ j j j P l-1 PmPm PlPl Parity Peer Query Answer j j i’,n’ PlPl LH* RS P2P Churn Management

33 Conclusion LH* RS P2P require at most one forward message when addressing error occur Is the fastest known SDDS and P2P key based addressing algorithm Protects efficiently against churn Allows to manage very large scalable files Should have numerous applications LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment

34 Current & Future Work LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Implementation of the peer node architecture and the tutoring functions  Using existing LH* RS prototype  Created by Rim Moussa & shown at VLDB 2004 Performance Analysis Variants

35 END LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment Work partly funded by the IST eGov-Bus project Thank you for Your Attention

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37 LH* RS P2P : A Scalable Distributed Data Structure for P2P Environment