Disjoint Multipath Routing to two distinct drains in a multi-drain sensor network Preetha Thulasiraman, Srinivasan Ramasubramanian and Marwan Krunz

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Disjoint Multipath Routing to two distinct drains
in a multi-drain sensor networkPreetha
Thulasiraman, Srinivasan Ramasubramanianand
Marwan Krunz

• Telvis Calhoun
• CS 8980-05 Dr. Li 11/13/2008

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Overview

• Motivation
• Authors present a multipath routing technique
  with minimal time complexity and messaging
  complexity.
• Experiment
• Authors compare new technique against an existing
  algorithm within a simulated environment
  containing up to 300 nodes.
• Conclusions
• The technique reduces average path length to a
  drain
• The technique reduces overall complexity

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Multipath Routing

• Multipath routing decreases average path length
  to a drain (sink).
• Reducing energy cost of forwarding data.
• Calculating multipath routes is expensive.
• Forwarding MPR packets requires large forwarding
  tables or message size.
• Authors use colored trees to minimize the
  complexity.

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Colored Tree

• Construct red and blue tree rooted at distinct
  drains.
• Each node has a next hop for each tree.
• Routing performed based on the link thus
  requiring no lookup.

Single Drain Network
Two Drain Network
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Disjoint Path Multi-Drain Problem (DRMD-2)

• Identify D trees each rooted at a distinct drain.
  
• Each node has 2 node disjoint paths to two
  drains.
• Algorithm
• Construct G from G adding virtual drain (v) with
  D links between v and drains.
• Route using tree pairs. Drain address 1-bit to
  identify tree used to forward packets.
• Each node is associated with a single tree. This
  requires a node to use a single drain on red and
  blue trees.

Tree where the paths for all nodes traverse drain
d3.
Tree where the paths traverse either d1 or d2.
Network with virtual drain
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Colored Tree Multiple Pair Problem (CTMP)

• There exists a tree-pair for every node where two
  paths to primary and one path to secondary that
  are node-disjoint.
• Bits required log D. Route table entries are 2
  D.

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Integer Linear Program

• Uses auxiliary graphs for each drain using
  virtual nodes (p,s)
• Virtual drain v that is connected to p and s
  virtual nodes of every aux graph.

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Distributed Algorithm for CTMP

• 3 steps
• Distributed depth first search (DFS) numbering of
  the nodes.
• Distributed path augmentation for computing the
  two trees.
• Choosing aux path that minimizes the sum of the
  two path lengths.
• Generalized low-point. The low-point path of a
  node n is n?i1?i2??ik?n (kgt0)
• Node n is the DFS parent of of node i1
• Node ij-1 is DFS-parent of ij
• DFS-index of n is lower than
• DFS-index of n is lowest among all possible
  lengths.

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DFS Numbering

• Number drains 1 through D. Highest number drain
  initiates node numbering.
• Compute generalized low point value (GLPV) and
  generalized low point neighbor (GLPN).
• Construct low point table containing low point
  paths to each drain.

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Distributed Path Augmentation

1. Arrange the neighbors in the neighbor list in
   increasing order of their DFS-indices.
2. On receiving a TOKEN message, initiate path
   search for each neighbor.
3. Every node forwards SEARCH message to every
   neighbor according to some rules. Flag nodes
   belonging to augmented path.
4. Forward TOKEN to flagged nodes in a reverse
   traversal.
5. Receive RETURN from all neighbors and then send
   RETURN to the parent node.

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Auxiliary Graph Selection

• Nodes choose the auxiliary graph that provides
  the minimum sum of the primary and secondary
  paths.
• Forwarded paths contain primary drain address and
  bit.
• 0 indicates the packet is transmitted over the
  tree to the primary drain.
• 1 indicates the packet is transmitted over the
  tree to one of the secondary drains.

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Example

• (a) Primary tree rooted at drain d3
• (b) Secondary tree rooted at either drains d2 or
  d1
• (c) Primary tree rooted at drain d2
• (d) Secondary tree rooted at drains d3 or d1
• (e) Primary tree rooted at drain d1 and
• (f) Secondary tree rooted at drains d3 or d2.

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Complexity of Distributed Algorithm

• Numbering phase
• O(L)
• Augmentation phase
• Each drain performs augmentation in parallel so
  complexity is O(L) and message complexity is
  O(DL)
• Graph selection is O(D)

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Experiment

• Compare performance to solution obtained by ILP
  using CPLEX 8.0 solver.
• ILP modeled using 20, 30, 40 and 50 nodes network
  with 3 drains.
• Evaluated distributed algorithm using random
  topologies of 50, 100, 200 and 300 nodes that
  employ 3,4 and 5 drains.
• More drains reduces average path length by 46.2
  for CTMP problem. 7.53-gt4.05
• Disjoint routing to distinct drains significantly
  outperforms disjoint routing to the same drain.
• Simulation with links of unequal costs. 10 random
  topologies for each scenario. Performance similar
  to those with equal costs.

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Conclusion

• Authors present a multipath routing technique
  with minimal time complexity and messaging
  complexity.
• Authors compare distributed CTMP solution against
  ILP within a simulated environment containing up
  to 300 nodes.
• Distributed technique reduces average path length
  to a drain
• Distributed technique reduces overall complexity

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References

• Thulasiraman, P. Ramasubramanian, S. Krunz, M.,
  "Disjoint Multipath Routing to Two Distinct
  Drains in a Multi-Drain Sensor Network," INFOCOM
  2007. 26th IEEE International Conference on
  Computer Communications. IEEE , vol., no.,
  pp.643-651, 6-12 May 2007