PeertoPeer Distributed Search

1
Peer-to-Peer Distributed Search
2
Peer-to-Peer Networks

• A pure peer-to-peer network is a collection of
  nodes or peers that
• Are autonomous participants do not respect any
  central control and can join or leave the network
  at will.
• Are loosely coupled they communicate over a
  general-purpose network such as the Internet,
  rather than being hard-wired together like the
  processors in a parallel machine.
• Are equal in functionality there is no leader or
  controlling node.
• Share resources with one another.
• Examples Napster, Kazaa, BitTorrent,

3
Search

• Lookup records in a (very large) set of key-value
  pairs.
• Associated with each key K is a value V.
• E.g.
• K might be the identifier of a document.
• V could be the document itself.
• If the size of the key-value data is small, we
  could use a central node that holds the entire
  key-value table.
• All nodes would query the central node when they
  wanted the value V associated with a given key K.

4
What if the table is too large?

• Solution Distribute the responsibility
• At any time, only one node among the peers knows
  the value associated with any given key K.
• Any node can ask the peers for the value V
  associated with a chosen key K.
• Desire
• The value of V should be obtained using few
  messages.

5
Chord Circles - Placement

• To place a node in the circle, we hash its ID i,
  and place it at position h(i).
• Key-value pairs are also distributed around the
  circle using hash function h.
• For a pair (K, V ) compute h(K) and place (K, V )
  at the lowest numbered node Nj such that h(K) ?
  j.
• In Fig.
• Any (K, V ) pair such that 42 lt
  h(K) ? 48 would be stored at N48.
• If h(K) is any of 57,58,. .. ,63,0,1, then (K, V
  ) would be placed at N1.

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(Inefficient) Search

• Assumption
• Each node knows its successor in the circle.
• Search
• For instance, if N8 wants to find V for key K
  such that h(K) 54, it can send the request
  forward around the circle until a node Nj is
  found such that j ? 54
• it would be node N56.
• Very inefficient!

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Links in Chord Circles

• To speed up the search, each node has a finger
  table
• Gives the first nodes found at distances around
  the circle that are a power of two.
• Suppose that the hash function h produces m-bit
  numbers.
• Node Ni has entries in its finger table for
  distances 1,2,4,8, . . . ,2m-1.
• The entry for 2j is the first node we meet after
  going distance 2j clockwise around the circle.
• Example Finger table for N8 is

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Search Using Finger Tables

• Suppose Ni wants to find (K, V ) where h(K) j.
• If (K, V ) exists, it will be at the
  lowest-numbered node that is at least j.
• Algorithm Idea
• Let Nk be the successor of Ni.
• Check if iltj?k. If yes, (K, V ) must be at Nk if
  it exists. So, end the search and ask Nk to send
  (K, V ).
• Otherwise, consult the finger table to find the
  highest-numbered node Nh that is less than j.
• Send Nh a message asking it to search for (K, V
  ).
• Nh behaves the same.

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Search Using Finger Tables Example

• Suppose N8 wants to find (K, V ), where h(K)
  54.
• Since the successor of N8 is N14, and
  54?9,10,,14, (K, V) is not at N14.
• N8 examines its finger table, and finds that all
  the entries are below 54.
• Thus it takes the largest, N42, and sends a
  message to N42 asking it to look for key K and
  have the result sent to N8.
• N42 finds that 54?43,44,,48 between N42 and
  its successor N48.
• Thus, N42 examines its own finger table, which is

10
Search Using Finger Tables Example

• The last node (in the circular sense) that is
  less than 54 is N51, so N42 sends a message to
  N51, asking it to search for (K, V ) on behalf of
  N8.
• N51 finds that 54 is no greater than its
  successor, N56. Thus, if (K,V ) exists, it is at
  N56.
• N51 sends a request to N56, which replies to N8.
• The sequence of messages is shown in Fig.

11
Adding New Nodes

• A new node Ni (i.e., a node whose ID hashes to i)
  wants to join.
• If Ni doesnt know any peer, it is not possible
  for it to join.
• However, if Ni knows even one peer, Ni can ask
  that peer what node would be Ni's successor
  around the circle.
• To answer, the known peer performs the algorithm
  as if it were looking for a key that hashed to i.
  
• The node at which this hypothetical key would
  reside is the successor of Ni. Suppose that the
  successor of Ni is Nj.
• We need to do two things
• Change predecessor and successor links, so Ni is
  properly linked into the circle.
• Rearrange data so Ni gets all the data at Nj that
  belongs to Ni.
• To avoid concurrency problems, we follow a
  procedure we will not cover here.