1. Other Structured P2P Systems CAN, BATON Lecture 4 1

2. CAN  A Scalable Content Addressable Network 2

3. 3 CAN (content-addressable network)  hash value is viewed as a point in a D-dimensional cartesian space  each node responsible for a D-dimensional “cube” in the space  nodes are neighbors if their cubes “touch” at more than just a point (more formally, nodes s & t are neighbors when s contains some [, ] and t contains [, ]) Example: D=2 1’s neighbors: 2,3,4,6 6’s neighbors: 1,2,4,5 Squares “wrap around”, e.g., 7 and 8 are neighbors expected # neighbors: O(D) 165 4 3 2 7 8

4. 4 CAN routing  To get to from choose a neighbor with smallest cartesian distance from (e.g., measured from neighbor’s center) 165 4 3 2 7 8 e.g., region 1 needs to send to node covering X checks all neighbors, node 2 is closest forwards message to node 2 Cartesian distance monotonically decreases with each transmission expected # overlay hops: (DN 1/D )/4 X

5. 5 CAN node insertion  To join the CAN: find some node in the CAN (via bootstrap process) choose a point in the space uniformly at random using CAN, inform the node that currently covers the space that node splits its space in half 1 st split along 1 st dimension if last split along dimension i < D, next split along i+1 st dimension e.g., for 2-d case, split on x-axis, then y- axis keeps half the space and gives other half to joining node 165 4 3 2 7 8 X Observation: the likelihood of a rectangle being selected is proportional to it’s size, i.e., big rectangles chosen more frequently 9 10

6. 6 CAN node removal  Underlying cube structure should remain intact i.e., if the spaces covered by s & t were not formed by splitting a cube, then they should not be merged together  Sometimes, can simply collapse removed node’s portion to form bigger rectangle e.g., if 6 leaves, its portion goes back to 1  Other times, requires juxtaposition of nodes’ areas of coverage e.g., if 3 leaves, should merge back into square formed by 2,4,5 cannot simply collapse 3’s space into 4 and/or 5 one solution: 5’s old space collapses into 2’s space, 5 takes over 3’s space 16 5 4 3 2 16 5 4 3 2 42 5

7. 7 CAN (recovery from) removal process  View partitioning as a binary tree of leaves represent regions covered by overlay nodes (labeled by node that covers the region) intermediate nodes represent “split” regions that could be “reformed”, i.e., a leaf can appear at that position siblings are regions that can be merged together (forming the region that is covered by their parent) 16 5 4 3 2 7 8 9 10 11 12 1314 109 8 7 2 4 5 3 13 12 14 11 61

8. 8 CAN (recovery from) removal process  Repair algorithm when leaf s is removed Find a leaf node t that is either s’s sibling descendant of s’s sibling where t’s sibling is also a leaf node t takes over s’s region (moves to s’s position on the tree) t’s sibling takes over t’s previous region  Distributed process in CAN to find appropriate t w/ sibling: current (inappropriate) t sends msg into area that would be covered by a sibling if sibling (same size region) is there, then done. Else receiving node becomes t & repeat 109 8 7 2 4 5 3 13 12 14 11 61 X 16 5 4 3 2

9. BATON  A Balanced Tree Structure for Peer-to-Peer Networks 9

10. Overlay Networks  Add additional routing protocol on top of network routing (i.e. TCP/IP)  Need to be resilient to node failures, intermittent connectivity Redundancy in data and metadata  Most popular is Distributed Hash Table (DHT) Pastry Chord

11. Chord Overview  Randomly assign each peer an ID between 0 and 2 m  Hash key to find ID for an item  Next peer after ID (mod 2 m )is responsible for storing item  Each peer has routing table to subsequent peers  Table is used for incremental routing

12. Chord Routing Example (m = 6) Figures poached from Stoica et al., “Chord: A Scalable Peer-to-peer Lookup Service for Internet Applications,” SIGCOMM 2001.

13. DHTs: The Good, the Bad and the Ugly  Good Efficient routing algorithms Easy to understand Simple replication methods  Bad Load balancing depends on good choice of hash function  Ugly Can only do exact ID lookups, since items are clustered in key space Would like to do range and prefix searches

14. Related Work  P-Grid (CoopIS’01) Based on a binary prefix tree structure.  Can not guarantee log N search step boundary  P-Tree (WebDB’04) Based on B+-tree structure and uses CHORD as overlay framework Each node maintains a branch of the B+tree  Expensive cost to keep consistence knowledge among nodes  Multi-way tree (DBISP2P’04) Each node maintains links to its parent, its siblings, its neighbors, and its children  Can not guarantee log N search step boundary

15. BATON Architecture Binary Balanced Tree Index Architecture  BATON: BAlanced Tree Overlay Network  Definition: A tree is balanced if and only if at any node in the tree, the height of its two subtrees differ by at most one.

16. Theorems  Theorem 1: The tree is a balanced tree if every node in the tree that has a child also has both its left and right routing tables full (*).  Theorem 2: If a node, say x, contains a link to another node, say y, in its left or right routing tables, parent node of x must also contain a link to parent node of y unless the same node is parent of both x and y. (*) A routing table is full if none of the valid links is NULL.

17. Node join  Example: new node u joins the network a ih kjmlon f d g e b c pqrs u u

18. Node join  Cost of finding a node to join: O(log N)  When a node accepts a new node as its child Split half of its content (its range of values) to its new child Update adjacent links of itself and its new child Notify both its neighbor nodes and its new child’s neighbor nodes to update their knowledge Cost: 6 log N

19. Node departure  When a node wishes to leave the network If it is a leaf node and there is no neighbor node having children, it can leave the network Transfer its content to the parent node, and update correspondence adjacent link Notify its neighbor nodes and its parent’s neighbor nodes to update their knowledge Cost: 4 log N If it is a leaf node and there is a neighbor node having children, it needs to find a leaf node to replace it by sending a FINDREPLACEMENTNODE request to a child of that neighbor node If it is an intermediate node, it needs to find a leaf node to replace it by sending a FINDREPLACEMENTNODE to one of its adjacent nodes

20. Node departure  Example: existing node b leaves the network a ih kjmlon f d g e c pqsu t b r r

21. Node departure  Cost of finding a leaf node to replace: O(log N)  When a node comes to replace a leave node Notify its parent and its neighbor nodes as in case of leaf node leaving: 4 log N Notify its new parent node, its new neighbor nodes, and the parent’s neighbor nodes: 4 log N Total cost: 8 log N

22. Fault tolerance  Node failure Nodes discovering failure of a node report to that node’s parent. The failure’s parent node will take responsibility for finding a leaf node to replace if necessary. Routing information of the failure node can be recovered by contacting its neighbor nodes via routing information of its parent.  Fault tolerance: failure node can be passed by two ways Through routing tables (similar to CHORD) - horizontal axis Through parent-child and adjacent links - vertical axis Specifically, even if all nodes at the same level fail, the tree is not partitioned

23. Network restructuring  Necessary in case of forced join or forced leave that is used in load balancing scheme  Network restructuring is triggered when the condition in the theorem 1 is violated  Network restructuring is done by shifting nodes via adjacent links No data movement is required Each shifted node requires O(log N) effort to update routing tables

24. Forced join  Example 1: network restructure is triggered as a forced join

25. Forced leave  Example 2: network restructuring is triggered as a forced leave

26. Index construction  Each node is assigned a range of values  The range of values directly managed by a node is Greater than the range managed by its left adjacent node Smaller than the range managed by its right adjacent node

27. Exact match query  Example: node h wants to search data belonged to node c, say 74 a ih kjmlon f d g e b c pqrts [0-5) [8-12) [17-23)[34-39)[51-54)[61-68)[75-81)[89-93) [5-8) [23-29)[54-61)[81-85) [12-17) [72-75) [45-51) [29-34)[39-45)[68-72)[85-89)[93-100)

28. Range query  Process similar to exact match query First, find an intersection with searched range Second, follow adjacent links to retrieve all results  Cost Exact match query: O(log N) Range query: O(log N + X) where X is the total number of nodes containing searched results

29. Data insertion and deletion  Insertion Follow the exact match query process to find the node where data should be inserted except that If it is the left most node and the inserted value is still less than its lower bound, or if it is the right most node and the inserted value is still greater than its upper bound, it expands its range of values to accept the new inserted value. In this case, additional log N cost is needed for updating routing tables  Deletion Follow the exact match query process to find the node containing data which should be deleted  Cost: similar to exact match query process O(log N) for both insertion and deletion

30. Load balancing  Load balancing process is initialized when a node is overloaded or under loaded due to insertion or deletion  2 load balancing schemes Do load balancing with adjacent nodes An overloaded node finds a lightly loaded node to share work load (only if the overloaded / under loaded node is a leaf node) A lightly loaded node is found by traveling through neighbor nodes within O(logN) steps. Once found, the lightly loaded node transfers its content to one of its adjacent nodes, forced leaves its current position, and forced joins as a child of the overloaded node. Network restructuring is triggered if necessary Similar process is applied to under loaded nodes  Cost: O(log N) for each node attending load balancing process

31. Load balancing  Example: node g is an overloaded node while node f is a lightly loaded node

32. Experimental study  Experimental setup Test the network with different number of nodes N from 1000 to 10000. For a network of size N, 1000 x N data values in the domain of [1, 1000000000) are inserted in batches 1000 exact queries, and 1000 range queries are executed CHORD and Multi-way tree are used to compare

33. Join and leave operations Cost of finding join node and replacement node Cost of updating routing tables

34. Insert and delete operations Cost of insert and delete operations

35. Search operations Cost of exact match query Cost of range query

36. Access load Access load for nodes at different levels

37. Effect of load balancing Average messages of load balancing operation Size of load balancing process

38. Effect of network dynamics Network Dynamics

39. Conclusion  BATON The first P2P overlay network based on a balanced tree structure Strengths Incur less cost of updating routing tables compared to other systems Support both exact match query and range query efficiently Flexible and efficient load balancing scheme Scalability (NOT bounded by network size or ID space before hand)

40. Thank you Q & A