1. Pastry Partially borrowed for Gabi Kliot

2. Pastry Scalable, decentralized object location and routing for large-scale peer-to-peer systems  Antony Rowstron (Microsoft Research)  Peter Druschel (Rice University)

3. Distributed Hash Table Map(Object-Id, Node-Id)  Pastry: ids are mapped to the node with closest node- id Goal: Reduce space complexity while marinating a reasonable time complexity  Pastry: O(Log(N)) space, O(Log(N)) lookup Chord – was taught in the lecture… Pastry Vs. Chord  Different technique – tables, algorithms, etc.  A proximity heuristic

4. Address Space 128 bit circular id space Assumes a random uniform distribution on node-ids Assumes a random uniform distribution on object-ids In short, Assumes diversity among correlated ids

5. Pastry Node State Base: 2 b = 4 Log 2 b 2 128 rows 2 b columns The address space is not full Still sharing prefix Chosen by proximity L closest ids L proximity closest ids (not used for routing) R[r,c] = node with largest matching prefix sized r followed by the digit c

6. Lookup Procedure If (destination is within range of our leaf set) forward to numerically closest member else let l = length of shared prefix let d = value of l-th digit in D’s address if (R[l,d] exists) forward to R[l,d] else // rare case forward to a (leaf-set node) such that (a) shares at least as long a prefix (b) is numerically closer than this node

7. Lookup Example d46a1c Look for (d46a1c) d462ba d4213f d13da3 65a1fc d467c4 d471f1

8. Proximity Perspective d46a1c Route(d46a1c) d462ba d4213f d13da3 65a1fc d467c4 d471f1 d467c4 65a1f c d13da3 d4213f d462ba Proximity space  The proximity distance traveled by message in each routing step is exponentially increasing (entry in row l is chosen from a set of nodes of size N/2 bl )  The distance traveled by message from its source increases monotonically at each step (message takes larger and larger strides) NodeId space

9. Self Organization – Join Seek (flood) for a nearby node with id A Obtain neighboring-set from A Ask A to lookup our id X Lookup arrives at Z with id closest to X Obtain leaf-set from Z, why? Obtain the i th row from the i th node in the lookup traversal to Z, why? Maintains reasonable proximity still, improve by exchanging information with the neighboring-set

10. Self Organization – Depart / fail Leaf-Set  Permanently monitored  Ask Routing Table  Lazy – When a node doesn’t respond  Complete the table slot from a node in the same row, if not found from higher rows Neighboring-Set  Permanently monitored and maintained

11. Performance Space Complexity O(log(N)) Time Complexity  Lookup – O(log(N)) Expected  Join – O(log(N)) Expected Short routes in terms of proximity (not necessarily shortest) Eventual safe delivery

12. More Details http://research.microsoft.com/~antr/PAST/pastry.pdf