Common approach

1
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)

2
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

3
Chord MIT

• Overlay
• Peers are organized in a ring
• Successor peer
• ltk, valuegt 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

4
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(log2N) 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

5
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)(n1/d) steps for lookup
• d dimension

6
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

7
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

8
Symphony Performance

• Each node has k O(1) long distance links
• Lookup
• Expected path length O(1/k log2N) hops
• Join leave
• Expected O(log2N) 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.

9
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)

10
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

11
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)

12
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 2i) 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

13
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