Labeling and Indexing Schemes and Algorithms for the Semantic Web

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Labeling and Indexing Schemes and Algorithms for
the Semantic Web
1 Stuckenschmidt, H. Vdovjak, R. Houben, G.
Broekstra, J. Index Structures and Algorithms
for Querying Distributed RDF Repositories 2
Christophides, V. Plexousakis, D. Scholl, M.
Tourtounis, S, On Labeling Schemes for Semantic
Web
Presentation for CSCI 8350 By Scott Patterson
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The Problem

• The Semantic Web is distributed by nature,
  therefore
• Information may be duplicated at different
  locations
• The information that is duplicated may be
  expressed in different ways
• The information desired from a query may be
  stored in fragments

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The Problem

• Suppose you would like to search for titles of
  articles written by employees of organizations
  that have projects in the area of RDF
• Realistically this information is not stored in
  one place. Perhaps there are there RDF stores
  (in this case databases) containing different and
  similar information.

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The Problem

• Suppose the first db contains information on
  articles, titles, authors, and their affiliations
• The second contains information about industrial
  projects, topics and organizations
• The third contains all the relevant information
  but is a research portal

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The Problem

• How can the information we desire be extracted
  and joined in such a way that..
• We have not lost any information
• We have not duplicated any information
• and it is done in a computationally efficient
  manner

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The Architecture

• Extend an existing RDF storage and retrieval
  system, Sesame
• Queries are passed from the query engine to SAIL
  (an RDF API) which abstracts from the repository
• In a distributed environment, the repositories
  may be implemented in different ways
• Hence the introduction of another RDF API between
  SAIL and the db

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The Architecture

• Now that the heterogeneity of the environment is
  abstracted we are back to the problem
• How to locate the relevant information, retrieve
  it, and put it together for an answer to our
  query
• For this another new component is added between
  Sesame and SAIL

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The Architecture

• This component is the Mediator SAIL
• The job of the Mediator is to determine where to
  send which parts of the query and how to optimize
  the query plan

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The Solution

• The solution to this problem has two parts
• First, to use join indices
• Second, find an algorithm that can efficiently
  optimize a query plan that consists of joins

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Join Indices

• Create additional database tables that contain
  the result of a join over a specific property
• Rather than computing a join, a system can simply
  access the index
• The property here is a path

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Join Indices

• Because the information that makes up a path may
  be distributed across different stores, it is
  necessary to use an index structure that contains
  information about sub-paths.
• A source index is used here to determine where
  instances of a path are stored.
• This determines where to forward the query

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Join Indices

• The join index hierarchy is an adaptation of join
  indices
• The root of the hierarchy is an index table for
  elements in the path p0, p1,pn-1 of
  length n
• The next level has two paths of length n-1
• The last level has n paths of length 1

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Join Indices

• The hierarchy contains information about every
  possible sub-path
• These sub-paths may later be combined to answer
  the query

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Join Indices

• From our running example we have
• P0..3 (author, affiliation, carriesOut, topic)
• P0..2 (author, affiliation, carriesOut),
  p1..3 (affiliation, carriesOut, topic)
• p0..1(author, affiliation),
  p1..2(affiliation, carriesOut),
  p2..3(carriesOut, topic)
• p0(author),
  p1(affiliation),
  p2(carriesOut),
  p3(topic)

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Remember The Problem

• Suppose the first db contains information on
  articles, titles, authors, and their affiliations
• The second contains information about industrial
  projects, topics and organizations
• The third contains all the relevant information
  but is a research portal

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Join Indices

• The time complexity of using the join index
  hierarchy is
• O(s n2) ,where s is the number of sources and
  n is the length of the path, which is polynomial
  time
• The length of the path is a significant factor

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Answering Algorithm

• The algorithm must do several things
• Determine all possible combinations of sub-paths
• For each combination determine the source
  containing the results for the sub-paths
• Join the results into one results for the
  complete path

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Answering Algorithm

• The algorithm must guarantee that all possible
  combinations of sub-paths have been investigated
• To do this, a tree-recursion algorithm is used
• Splitting a complete path into all possible
  combinations of sub-paths and then joining the
  results is not computationally reasonable

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Answering Algorithm

• The solution is to use the tree-recursion
  algorithm along with source information from the
  index hierarchy.

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Answering Algorithm

• This is an algorithm for a distributed system, so
  communications costs must be taken into account.
• Since it is over an IP network the communication
  costs will contribute significantly to the over
  all processing costs

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Answering Algorithm

• Data is joined by the Mediator, therefore
  minimization of the data that is transferred is
  important.
• There may be dependencies which allow those joins
  which do not contribute to the result to be
  pruned.
• Human interaction is necessary.

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Answering Algorithm

• Joins need to be ordered in such a way that the
  overall response time is minimized.
• This is an NP-hard problem.
• Evaluating all possible combinations of joins is
  impossible
• Therefore a Good Enough algorithm is used

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Answering Algorithm

• The objective of the algorithm now is to avoid a
  bad query plan and not to find the optimal query
  plan.
• In most cases the optimal plan only improves the
  solution marginally.
• In order to achieve this goal, experience from
  the database community is used

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Answering Algorithm

• A two phase strategy is applied
• Iterative Improvement (II)
• Simulated Annealing (SA)
• The II algorithm
• Randomly generates several solutions
• These are used as starting points in the
  traversal
• The traversal is done by applying a series of
  random moves from a predefined set

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Answering Algorithm

• The cost is evaluated for each move
• The best solution is kept in memory
• In the SA each sub-optimal solution is explored
  further
• Like the II, random moves are preformed
• Lower cost moves are accepted by the system
• Unlike the II, higher cost moves can also be
  accepted

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Answering Algorithm

• Acceptance of a higher cost move depends on the
  temperature of the systems and the cost
  difference
• This is because initially the system is hot and
  easily accepts moves which yield a higher cost
• This solution generates a Good Enough query
  plan and guarantees completeness of the result

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Labeling

• How can we label the information to increase the
  efficiency of subsumption queries?
• The data may be stored in a database, but we
  should try to visualize it as a tree or graph
• Labeling scheme should have a minimal complexity

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Labeling
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Labeling

• Bit-Vector
• Label is a vector of n-bits, n is the number of
  nodes
• A 1 bit in some position is used to uniquely
  identify nodes
• A node inherits bits from its ancestors
• This allows subsumption checking in constant time
• The construction of the Labels is linear to the
  number of nodes

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Labeling
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Labeling

• Prefix
• A node is labeled with the parent nodes
  identification
• This allows subsumption checking in constant time
• NCA can also be determined in constant time
• Labels can be created in Linear time

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Labeling
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Labeling

• Interval
• A node is labeled with an interval consisting of
  its preorder and postorder number or some
  variation
• For node u pre(start u), post(end u)
• An ancestor node of u is before u in preorder and
  after in postorder
• pre(v) lt pre(u) and post(v) gt post(u)
• Subsumption constant
  Labels linear to the number of nodes
  -variations may be polynomial

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Labeling
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Questions

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