Building Low-maintenance Expressways for P2P Systems

1
Building Low-maintenance Expressways for P2P
Systems

• Zhichen Xu and Zheng Zhang
• Presented By
• Swetha Boinepally

2
Overview

• What are Expressways ?
• CAN
• CAN construction
• Routing in CAN
• Overview of Expressway
• Building Expressway
• Routing with Expressways
• Tuning towards load balance
• On demand maintenance
• Analysis of routing
• Tuning towards best performance
• Conclusion

3
Introduction

• Expressway is an auxiliary mechanism to
  deliver high routing performance.
• Expressways are auxiliary data structures.

4
Real Life Expressways Vs. Expressways in P2P
Systems

• Expressways in P2P systems are analogous to the
  real world expressways.
• Attributes of expressways
• - Auxiliary mechanisms. Not a wholesale
  replacement of local
• routes.
• - Greater span per hop.
• - High bandwidth.
• Difference between real life expressways and
  expressways in P2P systems
• Expressways in P2P systems are
• - Self organized.
• - Self maintained.
• - Adaptive to changing network.

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Why CAN ?

• CAN has performance of O(N1/d)
• Expressways improves the routing performance to
  O(log N)
• Highly scalable
• Simple routing algorithm
• Low maintenance cost

6
Content Addressable Network(CAN)

• CAN is a distributed infrastructure which
  provides hash table like functionality.
• CAN organizes the logical space as a
  d-dimensional Cartesian coordinate space.
• Entire coordinate space is partitioned among all
  the nodes.
• Each node owns its individual zone within overall
  space.

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CAN construction

• All nodes are represented in the coordinate
  space.
• When a new node joins, it joins a node that is
  close to it in IP distance.
• The existing node will split its allocated zone
  into half.
• The neighbors of the split zone must be notified.
• When a node leaves the network, its zone should
  be taken over by one of its neighboring nodes .

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Example
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Routing in CAN

• CAN node maintains a coordinate routing table
  that holds the IP address and the virtual
  coordinates of each of its neighboring zones.
• A CAN message includes the destination
  coordinates. Using its neighbor coordinate set, a
  node routes a message towards its destination by
  simply forwarding to the neighbor with
  coordinates closest to the destination
  coordinates.

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Example

• We consider a 2-d Cartesian space with 16 equal
  zones.
• Each node has maximum of 4 neighbors.
• Maximum routing path length is 3 hops.

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D-dimensional Space

• For a d-dimensional space which is partitioned
  into n equal zones
• The average routing path length is
• (d/4)(n(1/d)) hops.
• of neighbors for an individual node is
• 2d.

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Scaling Results

• The previous results show that for a
  d-dimensional space, we can grow the number of
  nodes(zones) without increasing the per node
  state.
• The average routing path length grows in
  proportion to (n(1/d)).
• Thus the routing performance in CAN is
• O(n(1/d)).

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Overview of Expressways

• Expressways of CANs have routing tables of
  increasing span.
• The entire space is partitioned into zones of
  different spans with smallest zones correspond to
  the CAN zones and any other zones are called
  Expressway zones.
• Each node owns a CAN zone and is also a resident
  of the Expressway zone that encloses its CAN
  zone.
• Expressway zones and CAN zones are recorded in
  each node in data structure called Total routing
  table.

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Contd

• In this example, CAN zones are at level 3, four
  of neighboring CAN zones make one level 2
  expressway and four such level 2 zones make a
  level 1 zone.
• Total routing table of node 1 consists of the
  default routing table of CAN(plain arcs) and
  expressway routing tables(thick and long arcs)

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Contd

• Total routing table RT
• RT lt R0, R1, R2, . . . ., RLgt where RL
  corresponds to the nodes default routing table
  that CAN already builds.
• Ri(i0 to L-1) is called an Expressway routing
  table that has larger span. Smaller the i larger
  the span.
• For each neighboring expressway zone, the
  expressway routing table keeps the address of one
  or more nodes in that zone.
• In the previous figure, CAN zones are at level 3
  and each CAN zone is 1/64 th of entire Cartesian
  space.

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Building Expressways

• The algorithm for building expressway is
  Evolving snapshot.
• According to the algorithm, at regular intervals
  of system growth, snapshots of current routing
  table are taken.
• Each node takes the snapshot independently by
  observing its zone size, with which it may infer
  to what stage the system has grown.
• For node x, suppose the current zone size is
  x.R.Z and the target size is x.R(L-1).Z/K. if the
  xs current size shrinks to its target size then
  it takes a new snapshot by incrementing L. where
  K is the span of the expressway.

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Notations Used
18
Procedure for New Node Join

• When a node y splits with x, it inherits all
  entries of xs total routing table other than xs
  current routing table.
• Procedure when a node y joins node x
• y.RT ltx.R0,x.R1,,x.RL-1,y.RLgt
• repeat the procedure for testing for a new
  snap shot
• Both nodes test to see if its current zone has
  shrunken to 1/K th of its last snapshot.

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Algorithm to Test a New Snapshot

• Procedure for testing for new snapshot
• //executed by both x and y
• If (RL.Z lt RL-1.Z/K)
• RL1 RL
• RTltR0,R1,..,RL,RL1gt
• LL1

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Expressway Tree

• CAN can be thought as building a binary tree
  since each new node splits a random existing
  node.
• Total routing table can be found by walking down
  the tree from the root towards the node picking
  up the snapshot routing tables.
• Tree rooted by x when it joined system is called
  xs expressway tree.

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Routing

• If the destination point is within the current
  zone (RL.Z) then we can route it using the CANs
  default routing table.
• If the node is in some other zone, it iterates
  through the total routing table, starting from
  the one with largest span.
• It iterates until it finds a routing table whose
  space does not cover the destination.
• Suppose Ri is the routing table whose space does
  not cover the destination, then Ri is selected
  and the message will be routed according to Ri to
  one of Ris expressway neighbors.

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Pseudo-code for Routing With Expressway

• Route with Expressway
• If(pt?RL.Z)
• Return
• For(i0iltLi)
• If(pt?(Ri.Z))
• Route using Ri
• Route with Ri
• for(j0jltdj)
• if(ptltRi.Z.Lj ptgtRi.Z.Uj)
• Route to x?Ri.Nj that is close to pt
• Break

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Tuning Towards Load Balance

• Achieving load balance requires that a node z
  that routes to x in expressway routing, to have
  the option for replacing x with any node inside
  the xs expressway tree.
• Let Z.Ri be the routing table used to route to x
  and X be the xs expressway zone, then we pick a
  point pt in X and route to it. Whoever owns that
  zone now replaces x in Z.Ri. Here the point pt is
  selected randomly.
• of nodes that replace x is proportional to the
  size of xs Expressway tree and therefore is
  proportional to the of residents inside xs
  Expressway tree.
• Thus the algorithm will automatically balance the
  load among Expressways.

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Default Vs. Random Algorithms

• This figure show the simulation results reporting
  number of messages each node has to forward with
  default routing table and the routing table
  constructed using random selection.
• We see that with random selection, more of
  messages are forwarded

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On-demand Maintenance

• When a new node joins the network, it updates its
  expressway neighbors for the EW zones recorded in
  its total routing table. Such maintenance is
  proportional to the total levels of expressways,
  which is O(logkN).
• When a node departs, one of its neighbors will
  take over departed nodes responsibilities.
  However the departed node can be the expressway
  neighbor of multiple nodes and its EW functions
  need to be maintained by some other nodes.

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Contd

• Suppose node x departs from the network, and node
  y attempts to route to node x, then the request
  will timeout and node y tries to use the EW with
  smaller reach.
• Now node y picks up a point pt in the space of x
  recorded in the failed routing table, and route
  to it. If node z owns the zone in which the point
  pt lies then node z is now replacement of x to
  repair ys snapshot.
• On average the total of nodes that will update
  their routing table entries is the product of the
  total of expressway levels and the of
  neighbors in each level, which is O(d.logkN).

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Storage

• Let m be the of levels of EWs and mlogkN. The
  total routing table depth is m and as a result
  the storage for routing table increases m-folds.
• For example, if K4 and N220 (million nodes),
  then m is 10 and it takes only few hundred bytes
  to store the routing table. Therefore storage is
  not a concern.

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Routing with expressways

• Routing expressways involves at most m levels of
  CAN like routing.
• Routing algorithm will iterate through the table
  to get down to the level where the expressway
  zone doesn't cover the destination. It will the
  follow the CAN routing to reach an expressway
  zone that covers the destination.

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Analysis

• The average routing hops in any level are
  (d/3)K(1/d) hops and number of levels the
  routing will travel are logkN levels. Thus there
  are (logkN)(d/3)K(1/d) hops in the worst case.
• The bigger the K, the less levels of expressways
  there are and routing at each level is more
  expensive, so we need to find the optimal K.

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Contd

• Let f(x)(d/3).(x1/d).logxN
• Taking the derivative and equating it to zero
• f(x) 0 gt
• (d/3).(1/d.x(1/d-1).lnN/lnx
  x(1/d-1).lnN/(lnx)2
• on simplification we get 1/d1/lnx
• gt xed
• Thus the optimal K is ed and the optimal routing
  performance is
• f(x)(d/3).((ed)1/d).log(ed)N
  d/3.e.lnN/d e/3 lnN
• Thus the routing performance of CAN using
  expressways is O(lnN). And it is independent of
  choice of d.

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Expressway Performance Compared With Theoretical
Values

• In the figure, theoretical performance using EW
  is compared with results obtained using
  simulation.
• There are small deviations in these values.

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Expressway Performance Compared With CAN With
Different D

• In this graph, we can see that the EW performance
  with d1 outperforms the basic CAN with d5.

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Tuning Towards Best Performance

• Tuning towards network conditions
• Locating closest nodes using coordinate maps
• Route around congested node
• Tuning according to application needs

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Locating Closest Nodes

• Build maps of network coordinates, and utilizing
  the archival capacity of P2P system itself to
  store and maintain the maps in various zones in
  CAN.
• Any node can find a resident close to it in a
  given expressway zone Z by consulting the
  appropriate map.
• There is one map for each expressway zone in the
  system.

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Route Around Congested Node

• In Internet like dynamic environment, the traffic
  flow is unpredictable and the common problem to
  deal with is congestion.
• Congestion can be avoided by detecting the
  congested node, reporting and finding the
  alternate route.
• To find the appropriate expressway neighbor, each
  node will periodically update its map with the
  information about its load.

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Tuning According to Application Needs

• Reducing the per hop distance may not necessarily
  reduce the total delay.
• To account for the communicating patterns of
  application, the total routing table of node
  keeps the addresses of multiple nodes, instead of
  keeping the address of the node that is
  physically closest to it.
• While routing to a destination, we attempt to
  balance the per hop distance and the total number
  of logical hops to achieve overall small latency.
• Routing performance can be further improved by
  allocating some storage at each node to cache
  routes based on runtime behavior.

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Summary

• Using expressways the performance of routing in
  CAN is improved from O(N1/d) to O(ln N).
• The important attributes of P2P systems are to
  reduce maintenance cost, and to provide venues to
  tune the system to suit the application needs and
  the underlying network conditions. Such that it
  beats O(ln N) in practice.

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Thank You