Decentralized Location Services

1
Decentralized Location Services

• CS273 Guest Lecture
• April 24, 2001
• Ben Y. Zhao

2
Review Object Location

• Neighborhood covers
• Each server knows about all objects in its
  neighborhood
• Object implosion at root cover node
• Goals
• Given ID, Locate nearest object in network
• Do so w/o centralization

3
PRR (SPAA 97)

• Namespace large enough to avoid collisions (N,
  Log2(N) bits)
• Insert Object
• Hash Object into namespace
• For (i0, iltLog2(N), i)
• Insert entry into nearest node matches onlast i
  bits
• If no matching node, then pick node w/ i-1 bits
  with highest ID value

4
PRR97 Object Lookup

• Lookup object
• Traverse same nodes as insert, except searching
  for entry at each node
• For (i0, iltLog2(N), i)
• Search for entry in nearest node matching
  onlast i bits
• Expected length of pointer at ith node is 2i

5
PRR97 Reaching nodes

• Routing between successive nodes
• Pointer map required
• Forwarding for any object name
• Needs to be compact
• Reduce complexity, insert at node matching every
  n bits

6
PRR97 Limitations

• Setting up the pointer maps
• Uses global knowledge
• Lack of adaptability in dynamic systems
• Finding node with i matching bits
• How do you find node with highest ID value
• What happens as network changes
• Need to maintain deterministic way to find the
  same node over time

7
Tapestry

• Zhao, Kubiatowicz and Joseph
• Help from Hildrum, Rao, Zhuang, et al.
• A fault-tolerant wide-area location and routing
  application infrastructure
• Core location/routing based on PRR97
• Algorithmic and system extensions
• Decentralized dynamic algorithms
• Redundancy everywhere for fault-tolerance

8
What do we want

• A dynamic mapping algorithm
• Deterministic over network changes
• Globally consistent mapping
• Assumptions
• All nodes with same matching suffix contains same
  null/non-null pattern in next level of routing
  map
• Requires consistent knowledge of nodes across
  network

9
Dynamic Object Mapping

• Mapping object ID to deterministic sequence of
  nodes to store location ptrs
• At ith hop while routing to object ID
• Insert entry in local storage
• If no next node exists matching i1 digits
• Route on next highest indexed non-null pointer
• End node reached when no other pointers in rest
  of route map
• Else route to nearest such digit

10
Analysis

• Globally consistent deterministic mapping
• Null entry ? no node in network with suffix
• ?consistent map ? identical null entries across
  same route maps of nodes w/ same suffix
• Additional hops compared to PRR solution
• Reduce to coupon collector problemAssuming
  random distribution
• With n ? ln(n) cn entries, P(all coupons)
  1-e-c
• For nb, cb-ln(b), P(b2 nodes left) 1-b/eb
  1.8? 10-6
• of additional hops ? Logb(b2) 2
• Distributed algorithm with minimal additional hops

11
Border Cases

• Two cases
• A. If a node disappeared, and some node did not
  detect it.
• Routing proceeds on invalid link, fails
• No backup router, so proceed to surrogate routing
• B. If a node entered, has not been detected, then
  go to surrogate node instead of existing node
• New node checks with surrogate after all such
  nodes have been notified
• Route info at surrogate is moved to new node

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Algorithm Dynamic Insertion

• New node desires integration w/ ID 11111
• Step 1 copy route map recursively

?1111
??111
???11
????1
11111
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Dynamic Insertion cont.

• Step 2 Get relevant data from surrogateinform
  edge nodes of your existence
• Step 3 Notify neighbors to optimize paths

surrogate
?1111
..
...
...
..
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Summary

• Globally unique names
• Objects and nodes
• Randomly distributed
• Represented as digits of size b 2i
• Per node routing table size bLogb(N)
• N size of namespace, n of nodes
• Find object in Logb(n) hops
• Key properties
• Application controls modifications to object
• Overlay follows physical network distance

15
Alternatives P2P Indices

• Content Addressable Networks
• Ratnasamy et al.
• ACIRI / Berkeley
• Chord
• Stoica, Morris, Karger, Kaashoek, Balakrishnan
• MIT / Berkeley
• Pastry
• Druschel and Rowstron
• Rice / Microsoft Research

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Content-Addressable Networks

• Distributed hashtable addressed in d dimension
  coordinate space
• Routing table size O(d)
• Hops expected O(dN1/d)
• N size of namespace in d dimensions
• Efficiency via redundancy
• Multiple dimensions
• Multiple realities
• Reverse push of breadcrumb caches
• Assume immutable objects

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Chord

• Associate each node and object a unique ID in
  uni-dimensional space
• Object O stored by node with highest ID lt O
• Finger table
• Pointer for next node 2i away in namespace
• Table size Log2(n)
• n total of nodes
• Find object Log2(n) hops
• Optimization via heuristics

Node 0
0
1
7
2
6
3
5
4
18
Pastry

• Incremental routing like Plaxton / Tapestry
• Object replicated at x nodes closest to objects
  ID
• Routing table size b(LogbN)O(b)
• Find objects in O(LogbN) hops
• Issues
• Does not exploit locality
• Infrastructure controls replication and placement
• Consistency / security

19
Comparing Key Metrics
Chord
CAN
Pastry
Tapestry

• Properties
• Parameter
• Logical Path Length
• Neighbor-state
• Routing Overhead (RDP)
• Messages to insert
• Mutability
• Load-balancing

Base b
None
Dimen d
Base b
Logb(N)
O(dN1/d)
Logb(N)
Log2(N)
bLogb(N)
bLogb(N)O(b)
O(d)
Log2(N)
?O(1)
O(1) ?
O(1)?
O(1)
O(Log22(N))
O(dN1/d)
O(Logb2(N)) ?
O(Logb(N))
App-dep.
???
App-dep
Immut.
Good
Good
Good
Good
Designed as P2P Indices