Probabilistic Location and Routing

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Probabilistic Location and Routing

• INFOCOM 2002
• Sean C. Rhea, John Kubiatowicz

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Outline

• Introduce
• Algorithm Description
• Experimental Setup
• Results
• Future Work
• Related Work
• Conclusion

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Introduction

• Two important challenges
• How should we locate replicas
• How should we route queries to replicas
• Location-independent routing techniques
• CAN, Chord, Pastry, and Tapestry
• Location and routing operation require O(logN)

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Introduction (cont.)

• As the replica approaches the location of the
  query source, the performance of the existing
  algorithms quickly diverges from optimality
• Divergence
• A small amount of mis-routing in the local
  area can lead to a large divergence from
  optimality, since the optimal path is short to
  begin with

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Introduction (cont.)

• Our probabilistic location and routing alg. Is
  based on attenuated Bloom filters
• It is decentralized
• It is locality aware
• It follows a minimal search path
• It uses constant storage per server
• Attenuated Bloom filters allow us to achieve
• Quickly finding nearby replicas when they exist
• Finding every document even when replicas are
  scare

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Introduction (cont.)
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Algorithm Description

• Bloom Filters
• bit-vector of length w
• N different hash function
• False positive
• Width, the number of hash function, cardinality
  of the represented set

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Bloom filter
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Attenuated Bloom filter

• Attenuated Bloom filters of depth d is an array
  of d normal Bloom filters
• We associate each neighbor link with an
  attenuated Bloom filter
• The first filter in the array summarizes
  documents available from that neighbor
• The ith Bloom filter is the merger of all Bloom
  filter for all of the nodes a distance I through
  any path starting with that neighbor link, where
  distance is in terms of hops in the overlay
  network

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Attenuated Bloom filter
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The Query Algorithm

• To perform a location query, the querying node
  examines the 1st level of each of its neighbors
  attenuated Bloom filters
• If one of the filters matches, it is likely that
  the desired data item is only one hop away, and
  the query is forwarded to the matching neighbor
  closest to the current node in network latency
• If no filter matches, the querying node looks for
  a match in the 2nd level of every filter

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The Query Algorithm (cont.)

• As before, if a match is found, the query Is
  forwarded to the matching neighbor of lowest
  latency.
• This time, however, it is not the immediate
  neighbor who is likely to possess the data item,
  but one of its neighbors.
• This next neighbor is determined as before, by
  examining the attenuated Bloom filters of the
  current server

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The Query Algorithm (cont.)

• False positive
• Forward the request to the deterministic alg.
• The query can be returned to the previous server
  in the query path (DFS)
• Each query in the system contains a list of all
  the servers that it has already visited

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The Update Algorithm

• Every server in the system stores both an
  attenuated Bloom filter for each outgoing link
  (e.g. FAB in fig.3), and a copy of its neighbors
  view of the reverse direction
• The server calculates the changed bits in its own
  filter and in each of the filters its neighbors
  maintain
• It then send out these bits out to each neighbor

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The Update Algorithm (cont.)

• On receiving such a message, each neighbor
  attenuates the bits one level and computes the
  changes they will make in each of its own
  neighbors filter.
• These changes are sent out as well
• Etc

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The Update Algorithm (cont.)

• One problem with this algorithm
• The update will be propagated to some servers
  more than once (fig 3 a document was added to
  Node D)
• false positive rate
• Two distinct update filtering algorithm
• Destination filtering
• Source filtering
• When a deletion causes bits at any level of a
  Bloom filter to transform from one to zero, we
  must be careful to propagate this deletion to all
  appropriate nodes

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Experimental Setup

• We simulated it in conjunction with two different
  deterministic algorithms
• Home-node location
• a home-node server that keeps a set of pointers
  to every replica of the document
• Tapestry
• Assumption that every server and document in the
  system can be named with a unique,
  location-independent identifier

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Tapestry (cont.)

• Node-IDs for the node names and globally unique
  identifiers (GUIDs) for the documents
• Two major components
• A routing mesh
• A distributed directory service

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Tapestry Routing Mesh
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Publication in Tapestry
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Location in Tapestry
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Simulation Environment
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Simulation Environment (cont.)

• All stub to stub edges are 100Mb/s
• All stub to transit edges are 1.5Mb/s
• All transit to transit edges are 45Mb/s
• In our experiments, we focus on stub to transit
  domain bandwidth, since these inter-domain edges
  are the most bandwidth constrained in the system

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Experiment Descriptions

• Static experiments
• Dynamic experiments
• Based on whether the set of replicas in the
  system changes during the test

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Resultsprobabilistic update algorithm
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Static Experiments
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Static Experiments (cont.)
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Static Experiments (cont.)
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Static Experiments (cont.)
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Static Experiments (cont.)
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Static Experiments (cont.)
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Dynamic Experiments
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Dynamic Experiments (cont.)
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Dynamic Experiments (cont.)
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Future Work

• The design of algorithms to adhere to such
  restrictions while producing an overlay network
  in a self-organizing manner is thus an important
  component of our future work
• Since an update to a cache causes Tapestry to
  send only O(logN) message, whereas the
  probabilistic algorithm must send some amount of
  information to every server in its filters
  range, using these more advanced algorithms
  should only improve the bandwidth consumption of
  the probabilistic algorithm relative to Tapestry

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Related Work

• Bloom filters have long been used as a lossy
  summary technique. First to combine them into a
  compound, topology-aware data structure
• In 20, Bloom filters were used to improve the
  efficiency of distributed join operations by
  filtering elements without consuming network
  bandwidth.
• In 21, Aoki used Bloom filters to guide
  searches through generalized search trees

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Related Work (cont.)

• Both the Summary Cache and Cache Digests use
  Bloom filters to summarize the contents of a set
  of cooperating web caches
• The Secure Discovery Service (SDS) uses Bloom
  filters to route queries to appropriate services,
  such as printers or scaners

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Conclusion

• The algorithm is based on a new data structure we
  call an attenuated Bloom filter
• Furthermore, we have shown that our algorithm may
  be combined with a deterministic algorithm
• Finally, we have demonstrated that