Outline

1
Outline

• Problem definition, models, approaches, and
  analyses
• Preliminaries
• Our scheme for object routing and location

2
Problem definition, model, approaches, and
analyses

• Basic model A overlay network G (V,E) which is
  weighted and is often assumed metric shares
  objects (resources) O, V n, O m
• A node u requests for an object o held possibly
  by any other node v, i.e., u routes to or locates
  o
• Considers scalability, availability, load
  balance, locality, mobility, fault-tolerance

3
Problem definition, models, analyses, and
approaches (contd)

• Two approaches Plaxtons, Tapestry, Pastry, CAN,
  Chord v.s. Freenet, Gnutella, Morpheus, Napster
• The former guarantee availability while the
  latter do not
• The latter is more facilitating for search
  queries than the former
• Complexity measures
• Routing path length
• Stretch the ratio of the cost of the routing
  path the routing algorithm takes to the cost of
  the shortest routing path
• Routing table space

4
Preliminaries

• Hypercubes
• Routing path length O(log n)
• Routing table space O(log n)

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111
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5
Preliminaries (contd)

• Plaxtons (Tapestry, Pastry, Chord)
• Mapping object ID to node ID
• Unmapped digits need not to be fixed which makes
  it possible to bound the stretch (O(1))
• Relating Plaxtons (Tapestry, Pastry, Chord) to
  hypercubes
• Hypercubes cannot take edge costs into
  consideration

11X
111
1XX
XXX
Request for object 11111
6
Preliminaries (contd)

• CAN (Content-Addressable Network)
• Relating CAN to Plaxtons (Tapestry, Pastry,
  Chord)
• min O(d n1/d) O(log n) when d log n, which
  means arriving at destination in each dimension
  in constant hops rather than in n1/d hops

7
Our scheme for object routing and location

• CAN is a more general model in some way than
  Plaxton-like schemes, it achieves
• An average routing path length O(d n1/d) hops
• O(d) space, where d is the number of dimensions
• Yet, at each dimension, the routing does like an
  linear search (due to n1/d), which can be
  improved
• Idea with some bounded extra information, a
  distributed search structure can be built for
  each dimension which enables a more efficient
  routing

8
Our scheme for object routing and location
(contd) -- Idea Illustration
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9
Our scheme for object routing and location
(contd)

• Since tree structure does not provide each node
  equal probability responsible for routing
  requests, it becomes necessary to balance each
  nodes load
• This balancing task is made possible for
• Each node participates in d different binary
  trees at the same time
• It has a height of its position in each tree
• An average routing path length O(d log n1/d)
  O(log n) hops
• Routing table space O(d)

10
Our scheme for object routing and location
(contd)

• The stretch is an issue which is tackled by
  Topologically-sensitive construction of the
  overlay network and other optimizations in CAN
• Yet, CAN does not provide a formal proof to bound
  the stretch instead, it gives simulation results
• We still work on this stretch issue
• Other interesting related issues include
• Search ability
• Handling mutable objects
• Security