Transcript DHT: Past, Present, and Future

Common approach
1. Define space: assign random ID (160-bit) to each node
and key
2. Define a metric topology in this space,
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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
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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
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Efficiency
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Size of Routing Table
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Lookup, insertion, deletion
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
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Rigid routing table
 Requires higher maintenance costs – need to detect and
fix failures immediately
 Complicates recovery
 Preclude proximity-based routing
Chord: MIT
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Overlay:
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Peers are organized in a ring
Successor peer
<k, value> is stored on the
successor of k
Routing:
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Finger Table:
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More info for near part of the ring
Large jumps, then shorter jumps
Resembling a binary search
Chord: Characteristics
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Efficient directory operations
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Analysis
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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
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insertion, deletion, lookup
Node join/leave induces state change on other nodes
Rigidity of Routing Table (in original proposal):
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For a given network, there is only one optimal/ideal state
Unique, and deterministic
CAN: Berkeley
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Overlay:
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Routing:
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Each peer maintains info about neighbors
Greedy algorithm for routing
Routing table d information
Joining
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A virtual d-dimensional Coordinate space
Each peer is responsible for a zone
chose random point, split its zone
Performance Analysis:
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Expected: (d/4)(n1/d) steps for lookup
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d: dimension
Pastry: Rice
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Circular namespace
Routing Table:
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Routing:
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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.
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
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Distributed Hashing in a Small World
Like Chord:
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Overlay structure: ring
Key ID space partitioning
Unlike Chord:
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Routing Table
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Link to immediate neighbor (replicate for reliability)
k long distance links for jumping (not replicated)
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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
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Each node has k = O(1) long distance links
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Lookup:
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Join & leave
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Expected path length: O(1/k * log2N) hops
Expected: O(log2N) messages
Comparing with Chord:
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Discard the strong requirements on the routing table (finger
table)
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Idea that has been incorporated in Chord in a different way.
Kademlia: NYU
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Overlay:
 Node Position:
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Service:
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shortest unique prefix
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 subtrees where p resides.
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Share the prefix with p
Magnitude of distance (XOR)
k: replication parameter (e.g. 20)
Kademlia:
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Comparing with Chord:
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Like Chord: achieving similar performance
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Routing table size: O(logN)
Lookup: O(logN)
Lower node join/leave cost
Deterministic
Unlike (the original) Chord:
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Flexible Routing Table
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Given a topology, there are more than one routing table
Symmetric routing
Skip Graphs: Yale
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Based on “skip list” [1990]
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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:
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Skip List is not suitable for P2P environment
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No redundancy, Hotspot problem
Vulnerable to failure and contention
Skip Graph: Extension of Skip List
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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
Skip Graph:
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Performance:
 Since the membership vector is random, the performance
analysis is also probabilistic.
 Expected Lookup cost:
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Insertion:
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O(log n) messages (conclusion from skip list)
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