Plaxton%20Routing

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Plaxton Routing
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Introduction

• Plaxton routing is a scalable mechanism for
  accessing nearby copies of objects.
• Plaxton mesh is a data structure that allows
  messages to locate objects and route to them
  across an arbitrarily-sized network, while using
  a small constant-sized routing map at each hop.

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Role of each node

• Each node serves as
• a server,
• a client, and
• a router.

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Object and node names

• In an n-node Plaxton mesh, both objects and
  nodes have randomly chosen names (better call the
  them labels) of size log n bits independent of
  their location and semantic properties

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Important issues

• Routing to a node / object
• Reading an object
• Inserting an object
• Deleting an object
• Each node has a small routing table and a set
  of pointers pointing to nodes containing objects

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Routing table

• Each routing table has entries for
• primary neighbors,
• secondary neighbors and
• (3) Back pointers

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Routing table (1)
0
1
xxxxx 0 xxxxx 1
xxxx 0 0 xxxx 1 0
xxx 0 00 xxx 1 00
xx 0 000 xx 1 000
x 0 0000 x 1 0000
0 00000 1 00000
The primary neighbors in the routing table of
node 000000. X means wildcard. However,
neighbors with least communication cost are the
preferred primary neighbors. Up to a
known constant of neighbors in each slot can be
secondary neighbors
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Routing table (2)
0
1
2
3
x x 0 x x 1 x x 2 x x 3
x 0 0 x 1 0 x 2 0 x 3 0
0 0 0 1 0 0 2 0 0 3 0 0
Let N be a power of B2b. The above table is for
b2 and N64. The routing table will have at most
B.logBN entries for the primary neighbors
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Routing table (3)

• From each node x, there is a back
• pointer to another node y if x is a
• primary neighbor of y. It simplifies
• the searching of the root of an object
• by crawling backwards.

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Suffix routing

• Each node incrementally relays the messages to
  the destination id digit by digit, like
• 1 --gt 31 --gt 031 --gt 2031
• Each step picks a neighbor whose suffix has the
• largest match with that of the destination node,

Note that suffix and prefix routing are equivalent
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Another example of routing

• Example Octal digits, 218 namespace, 005712 ?
  627510

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Inserting an object

• A server S publishes that it has an object O by
  routing a message to the root node of O The
  root node is identified by applying a hash
  function on O. A real node whose id matches with
  this hash by the maximum number of trailing bits
  is the root of O.
• The publishing process consists of sending a
  message toward the root node. At each hop along
  the way, the publish message stores location
  information in the form of a mapping
  ltAObject-ID(O), y Server-ID(S), k Cost of
  accessing the object from that node.gt

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Inserting an object

Pointer to O
Secondary neighbors
Object O
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Insertion continued

• Where multiple copies of objects exist, only the
  reference to the closest object is saved at each
  hop to the root. The insertion procedure
  maintains this invariant. This is where the cost
  component of the pointers comes in.

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Inserting an object

Copy of O
Object O
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Deleting an object

Steps similar to insertion. The pointers should
be updated to reflect access to the closest copy.
Copy of O
Object O
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Read

Read tries to locate the root of the object. If a
pointer to O is discovered en route, then the
object is retrieved following that pointer
Copy of O
Read
Object O
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Benefits and Limitations

• (-) While the intermediate hops are not
  absolutely necessary, the unique root node serves
  a critical purpose. The downside of having a
  unique root is that it becomes a single point of
  failure.
• (-) Assumes the network to be static. Does not
  handle topology changes.

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Benefits and limitations

• Simple fault handling
• 1234 --gt 1238 --gt 1278 --gt 1678 --gt 5678
• 3128 --gt 3178 --gt 3678
• Optimal routing distance of O(log BN) between
  any pair of nodes