Common approach 1. Define space: assign random ID (160-bit) to each node and key 2. Define a metric topology in this space,  that is, the space of keys and node IDs 3. Each node keeps contact information to O(log n) other nodes 4. Provide a lookup algorithm, which maps a key to a node  i.e., find the node, whose ID is closest to a given key  the metric identifies closest node uniquely 5. Store and retrieve a key/value pair at the node whose ID is closest to the key (ro alternative functionality)

DHT: Comparison axes Efficiency  Lookup, insertion, deletion Size of Routing Table  How much state information maintained on each peer  O(n), O(log N) or O(1)  Tradeoff: Larger state  higher maintenance cost (but faster lookup) Flexibility of Routing  Rigid routing table Requires higher maintenance costs – need to detect and fix failures immediately Complicates recovery Preclude proximity-based routing

Chord: MIT Overlay:  Peers are organized in a ring  Successor peer  is stored on the successor of k Routing:  Finger Table: More info for near part of the ring Large jumps, then shorter jumps Resembling a binary search

Chord: Characteristics Efficient directory operations  insertion, deletion, lookup Analysis  O(logN) routing table size  O(logN) logic steps to reach the successor of a key k  O(log 2 N) for peer joining and leaving High maintenance cost  Node join/leave induces state change on other nodes Rigidity of Routing Table ( in original proposal ) :  For a given network, there is only one optimal/ideal state  Unique, and deterministic

CAN: Berkeley Overlay:  A virtual d-dimensional Coordinate space  Each peer is responsible for a zone Routing:  Each peer maintains info about neighbors  Greedy algorithm for routing  Routing table d information Joining  chose random point, split its zone Performance Analysis:  Expected: (d/4)(n 1/d ) steps for lookup d: dimension

Pastry: Rice Circular namespace Routing Table:  Peer p, ID: IDp  For each prefix of IDp, keep a set of peers who shares the prefix and the next digit is different from each other. Routing:  Plaxton algorithm  Choose a peer whose ID shares the longest prefix with target ID  Choose a peer whose ID is numerically closest to target ID Exploit the locality Similar analysis properties with Chord

Symphony: Stanford Distributed Hashing in a Small World Like Chord:  Overlay structure: ring  Key ID space partitioning Unlike Chord:  Routing Table Link to immediate neighbor (replicate for reliability) k long distance links for jumping (not replicated)  Long distance links are built in a probabilistic way  Neighbors are selected using a Probability Distribution Function (pdf)  Exploit the characteristics of a small-world network  Dynamically estimate the current system size

Symphony: Performance Each node has k = O(1) long distance links  Lookup: Expected path length: O(1/k * log 2 N) hops  Join & leave Expected: O(log 2 N) messages Comparing with Chord:  Discard the strong requirements on the routing table (finger table) Idea that has been incorporated in Chord in a different way.

Kademlia: NYU Overlay:  Node Position: shortest unique prefix  Service: Locate closest nodes to a desired ID Routing:  “based on XOR metric”  keep k nodes for each sub-tree which shares the root as the sub- trees where p resides. Share the prefix with p Magnitude of distance (XOR) k: replication parameter (e.g. 20)

Kademlia: Comparing with Chord:  Like Chord: achieving similar performance Routing table size: O(logN) Lookup: O(logN) Lower node join/leave cost Deterministic  Unlike (the original) Chord: Flexible Routing Table  Given a topology, there are more than one routing table  Symmetric routing

Skip Graphs: Yale Based on “skip list” [1990]  A randomized balanced tree structure organized as a tower of increasingly sparse linked lists  All nodes join the link list of level 0  For other levels, each node joins with a fixed probability p  Each node has 2/(1-p) pointers  Average search time: O(log N) (same for insert, delete)

Skip Graph: Skip List is not suitable for P2P environment  No redundancy, Hotspot problem  Vulnerable to failure and contention Skip Graph: Extension of Skip List  Level 0 link list builds a Chord ring  Multiple (max 2 i ) lists for level i (i = 1, … logn)  Each node participate in all levels, but different lists  Membership vector m(x): decide which list to join  Every node sees its own skip list

Skip Graph: Performance:  Since the membership vector is random, the performance analysis is also probabilistic.  Expected Lookup cost: O(log n) messages (conclusion from skip list)  Insertion: same as search, but more complicated due to the concurrent join Overall about skip graph:  Probabilistic (like Symphony)  Routing table is flexible  Given the same participating node set, no fixed network structure