Constrained Random Walks on Random Graphs: Routing Algorithms for Large Scale Wireless Sensor Networ

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Constrained Random Walks on Random Graphs
Routing Algorithms for Large Scale Wireless
Sensor Networks
Sergio D. Servetto, Cornell University
Guillermo Barrenechea, Ecole Polytechnique
Federale de Lausanne

• Presented by Guangyu Dong

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Outline

• Contribution
• Motivation Background
• Related Work
• Random Walk Approaches
• For regular and static graphs
• For irregular and static graphs
• For dynamic graphs
• Summary Comments

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Contribution

• A routing protocol for WSN that tries to do load
  balancing among intermediate nodes.
• Making use of multiple paths that exist from
  source to destination by making local packet
  forwarding decisions A novel approach to
  implicitly maintain multipath
• Current algorithm is only valid for grid-topology
  sensor network

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Motivation

• Consider the routing in a large-scale WSN with
  unreliability and dynamics
• A single node has limited capacity
• The unique characteristics of WSN calls for
  multipath routing techniques
• Searching for possible routes?
• Route creation and destruction?
• Random walk approach use an implicit way to solve
  these two problems

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Multiple Paths Routing

• Advantages
• Minimize critical points of failure
• Achieve load-balancing
• Disadvantages
• More energy consumption
• Not Clear
• Performance?
• Security?

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Ways to Do Multipath Routing

• Highly-resilient, energy-efficient multipath
  routing
• Routes packet through a primary path while
  maintaining several other paths as backup.
• Trajectory-based routing
• Each time source can randomly select a path for
  the packet
• Stateless
• SPEED
• Each packet has an unanticipated path.
• Stateless
• Is it really a multipath routing protocol?
• Random Walk
• Packet goes to a random direction at each node
• Not stateless

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Random Walk Approach

• Decentralized algorithms
• Complexity independent of the size of the network
• Dependence on the state of other nodes decays
  with separation distance
• Taking advantage of a vast number of multiple
  paths without explicitly listing them.
• Walking is constrained
• Packets visit nodes on short (low delay) routes??
• The number of packets that visit a node is
  independent of the particular node

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Assumptions and goals

• Infinite lifetime via renewable energy source
• Goal is to preserve energy to maximize node
  throughput while still alive
• As opposed to finite lifetime where the goal is
  to preserve energy to prolong existence of the
  network
• So will it still work when some kind of power
  control mechanism is used? For example, ASCENT or
  SPAN?
• The network is a grid
• The approach has a big dependence on graph
  structure
• No straightforward way to extend to a random
  graph
• Every node know its distance to source and
  destination

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Forwarding Decision based on PDF
u1
p1
u2
p2
v
..
pn
un
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Forwarding Decision in Grid
u4
p4
p1
v
u3
u1
p3
i,j
p2
u2
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Notation and Terminology

• N(v)u1,,un_v-neighbors of v
• ?vp1,,pn_v-pdf over neighbors of v
• GNgrid of size NxN
• D(l)-set of nodes on lth diagonal
• dei,j-distance from node i,j to nearest
  boundary node
• Expansion region packets move across diagonals
  with increase in number of nodes (decrease in
  pkt/node density)
• Compression region opposite of expansion

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Graph GN
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Expansion Compression Regions
Compression Region
Expansion Region
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Regular, static graphs (RSG)

• Network is grid such that each interior node has
  4 neighbors
• Constraints
• (c.1) Packet will not go backward
• (c.2) For nodes on a same diagonal, they must be
  visited equally often

The diagonals close to source and destination
only have a few nodes. Does it still make sense
to do load balancing?
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Sampling pdf for uniform packet distribution

• A packet at node i,j makes a binary decision to
  move to i1,j or i,j1 (c.1) with some
  probability p (by convention, to node closer to
  boundary)

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RSG Examples (N4)

• In the expansion stage, packet is more likely to
  be forwarded toward the boundary
• In the compression stage, packet is more likely
  to be forwarded apart from the boundary
• All possible paths have the same length

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Simulation Results (RSG)
A Random walk based on flipping a fair coin.
A Random walk based on RSG algorithm
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Distributed Computation of Coordinates

• Each node simply needs to know its own
  coordinates
• Find coordinates using Distributed Bellman Ford
  algorithm (local message exchange)
• Only good for a grid
• An initializing process necessary
• Introduces delay for initial packets

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Irregular, static graphs (ISG)

• Same as RSG but delete a random set of nodes
  permanently
• Impossible to achieve exact load balancing
• Use node labels (s,d)( routes to source,
  routes to destination)
• Can compute labels using recursion
• number of routes to a node is the sum of the
  numbers of routes at the two previous nodes
• Still a GRID!

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Example of Node Labels (N4)
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Forwarding pdf on a best-effort basis

• The probability that v will forward packet to the
  node (s1, d1) and (s2, d2)
• Pex (s lt d) Packet more likely forwarded to node
  with less source routes
• Pcmp(sgtd) Packet more likely forwarded to node
  with more destination routes

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ISG Examples (N4)
Ideal Case Equivalent to RSG
General Case
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Simulation Results (ISG)
A Random walk based on flipping a fair coin.
A Random walk based on ISG algorithm
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Dynamic Graphs (DG)

• Same as ISG but nodes turn ON/OFF independently
  over
• When a node changes state the one-hop neighbors
  change labels and possibly trigger further label
  changes
• More than half of the NN nodes will be affected
• Packet may be routed to a dead end due to delayed
  propagation of labels change, which will result
  in packet delay or loss.
• Concerns
• Delays in propagating updates
• Sensitivity to inaccuracies in labels

Remember the first assumption?
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The Overhead

• A large number of nodes need to keep a state for
  each stream
• An initializing process to compute labels for all
  nodes
• Beacon messages exchanged between neighboring
  nodes
• Check if neighbors are alive
• Exchanging labels
• State change of a node will affect a large part
  of the network. The degree of influence depends
  on the distance between changing node and
  source/destination.

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Simulation Results (DG)
A Random walk based on DG algorithm
A Random walk based on flipping a fair coin.
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More Simulation Results (DG)
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Open Issues

• Extends to general graph?
• Each node has arbitrary number of neighbors
• How to trade off between delay and load
  balancing?
• The overhead to compute and maintain the labels
  depends on how many nodes are in the rectangle
  area
• Design algorithm under the same principles
• Pex (s lt d) Packet more likely forwarded to node
  with less source routes
• Pcmp(sgtd) Packet more likely forwarded to node
  with more destination routes

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Summary Comments

• A decentralized random walk algorithm to do
  multipath routing
• Highly topology dependent algorithm is hard to
  extend to generally random graph
• Mobility not addressed
• All intermediate nodes have to keep routing state
  (NN) with considerable overhead
• A large number of nodes will be affected when a
  node switch between ON/OFF.
• An unrealistic energy model
• Inappropriate for multiple or dynamic packet
  streams

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GS3 Scalable Self-configuration and Self-healing
in Wireless Networks

• Hongwei Zhang, Anish Arora
• Computer Science Department
• The Ohio State University3

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Outline

• Contributions
• System models and goals
• GS-3 Algorithms
• For static network
• For dynamic network
• For dynamic and mobile network
• Problems
• Conclusion

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Contributions

• An algorithm aiming to organize wireless network
  into a ideal cellular hexagonal structure
• Self-healing under perturbations
• The clustering criteria, Geographic radius , is
  taken into consideration which many previous
  works didnt
• Scalability in large scale multi-hop wireless
  networks achieved by divide and conquer strategy

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Geographic Radius Cluster
Density of wireless network increases
Cluster with fixed radius
Radius is limited by maximum transmit range
Head Graph
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Related Work

• SPAN ASCENT
• Kind of clustering protocol (active node is
  cluster head)
• No big node
• For power control purpose, other nodes will sleep
• What if other nodes dont sleep?
• Can GS-3 be used for power control?
• Many Other Clustering Algorithms
• Geographic radius or Logical radius
• Local or Global self-stabilizing
• Some of them are for energy saving

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Cellular Structure
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System Models

• Node Distribution Assumption
• there are multiple nodes in each circular area of
  radius Rt (radius tolerance)
• Every node know its location
• Wireless Transmission Assumption
• Nodes adjust the transmission range
• Message transmission is always reliable
• Perturbation Models
• Dynamics nodes leaving, joins, deaths and state
  corruptions
• Mobility nodes movements.
• Perturbation Frequency
• Joins, leaves and death are unanticipated and
  rare, while node death is predictable
• The probability that a node moves distance d is
  proportional to 1/d

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Goals

• Each cell has radius of Rc (c is a function of
  Rt)??
• Each node in at most one cell
• A node in a cell if and only if its connected to
  the big node
• Number of children for each node in head graph is
  bounded (6)
• Self-healing in the presence of dynamics and
  mobility

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Definitions
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Algorithm for Static Networks

• No perturbation, no Rt gap
• Always H0 starts to be a head
• A head search for new heads in search region
• For H0, the search region is the whole 1-band
• Cell heads in search region are selected by i
• Nodes not selected as head choose their best heads

Will a node in k-band always have a parent from
(k-1)-band?
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Dynamic Network

• Perturbations
• Joining, leaving and death of nodes
• State corruption
• Rt gap
• Maintenance Mechanisms
• Head shift
• Cell shift
• Cell abandonment
• State check

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Algorithm for Dynamic Network

• Head selection same as GS-3 S
• Rt gap
• No head is selected
• Nodes become associates of neighboring cells
• Parent does periodical check
• Node join
• Try to find the best head
• If fails, try to find a potential head from
  associates
• If still fail, retries later.
• If a head is announcing itself, it selects this
  head as its head
• Node leaves or dies
• Intra-cell maintenance head shift, cell shift,
  cell abandon
• Inter-cell maintenance cell is monitored and
  recovered by parent and children heads if
  intra-call operation fails
• It the parent fails then the children finds other
  parents

Why not RtR?
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Cell Maintenance

• Cell will be abandoned when distance between IL
  and IL of some neighbor is beyond v3R-2Rt,
  v3R2Rt. (Rt gap!!)
• Abandoned cell will be restored later if possible
• The whole head graph will slide as a whole?
• Traffic load cannot be uniform
• Density varies across the network
• Central cell usually will not shift

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Algorithm for Dynamic Network (cont)

• Associate node always tries to find better head
• Head node always tries to find better parent
• State corruption (done by head)
• Periodical sanity checking (for invariants and
  fixpoint) on hexagonal relation.
• If checking fails, ask neighboring heads to check
  their state
• If all neighboring heads are valid, its state is
  corrupted, then node becomes an associate
• Otherwise, cannot decide????
• What if perturbations are not isolated??
• Will the algorithm still converge?
• Need theoretical verification or validation from
  simulations

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Problems

• Continuous Rt gap? (see next page picture)
• A connectable node is possibly not connected to
  the big node. So the third goal cannot be
  achieved
• How can we guarantee a safe leaving?
• Whats the transmission range of associate node
  and head node? Is there difference between them?

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Coutinuous Rt Gap
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Mobile Dynamic Network

• Small node movements leaves at old location,
  joins at new location
• Big node movements
• The closest head becomes the proxy of big node
• The proxy becomes the root of the head graph

What if big node moves to a null cell?
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Example of Big Node Movement
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Problems

• How to put all these complicated mechanisms
  together?
• What if perturbations are not isolated? Will the
  algorithm still converge??
• Control overhead
• Need to be validated by simulations

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Summary Comments

• Algorithm tries to organize wireless network into
  a ideal cellular hexagonal structure with fixed
  cell radius
• Try to do self-healing when assuming isolated
  perturbations
• Some of the mechanisms are not likely to work
• A complicated theoretical protocol without clear
  analysis or validation by simulation result
• What kind of application can we run on this
  structure?
• Whats the overhead to maintain this structure?

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Roads of Developing Algorithm