A Summary of XISS and Index Fabric

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A Summary of XISS and Index Fabric

• Ho Wai Shing

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Contents

• Definition of Terms
• XISS (Li and Moon, VLDB2001)
• Numbering Scheme
• Indices Stored
• Join Algorithms
• Index Fabric (Cooper et al, VLDB2001)
• Patricia
• Balanced Trie
• Raw Path Index

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Definition of Terms

• Absolute Path Expression (APE)
• the path which start from root, each step is a
  traversal of child axis or attribute axis, no
  wildcards
• e.g., /, /A/B, /A/_at_C

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Definition of Terms

• Regular Path Expression (RPE)
• may start from root or not,
• may traverse different axes (restricted to child,
  descendant-or-self, attribute for discussions
  since they are the most commonly used ones)
• may contain wildcards
• e.g., //, /A//C, /A/_/B, //A/B//C/D/_at_E

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XISS

• XISS XML Indexing and Storage System
• by Li and Moon, published in VLDB 2001, with
  title Indexing and Querying XML Data for Regular
  Path Expressions
• decomposes and stores XML documents in the
  indices
• can answer regular path expressions

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XISS - General Idea

• solve RPE by decomposing RPE into these 5 basic
  subexpressions
• element retrieval
• attribute retrieval
• steps involve an element and an attribute
• steps involve two elements
• a Kleene Closure of another subexpression

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XISS - General Idea

• each subexpression is solved by its own method
• element index lookup
• attribute index lookup
• EA-join
• EE-join
• KC-join

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XISS - General Idea

• result lists from the subexpressions are joined
  to produce the final result
• to make this decomposition and join efficient, an
  efficient method to determine ancestor-descendant
  relationship is needed
• XISS uses an extended preorder based numbering
  scheme

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XISS - Numbering Scheme

• number all the nodes with a ltorder, sizegt tuple
• order is assigned based on an extended preorder
  traversal
• size can be imagined as the size of the subtree
  rooted at that node

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XISS - Numbering Scheme

• The rules for number assignment
• if x precedes y in the preorder traversal,
  x.order lt y.order (preorder)
• if x and y are siblings, either x.order x.size
  lt y.order or y.order y.size lt x.order(siblings
  wont overlap)
• if x is an ancestor of y, x.order lt y.order lt
  x.order x.size (ancestor contains descendant)

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XISS - Numbering Scheme

• Actual Assignment
• uses heuristics to reserve some space between
  orders
• reserve more space to the sizes for future node
  insertions
• attributes are place before sibling elements

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XISS - Index Organization

• There are 5 indices
• Name Index
• Element Index
• Attribute Index
• Structure Index
• Value Table

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XISS - Name Index

• maps element or attribute name to a name
  identifier (or nid)
• nid is used for further query evaluation
  representing that element or attribute
• reduce the time for string comparison in further
  index lookup
• stored in a B-tree

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XISS - Name Index
Name
nid
B-tree
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XISS - Value Table

• stores all the string values of the XML document

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XISS - Element Index

• input nid, output list of element records
• implemented by a B-tree
• leaves are pointers to list of document ID (did),
  each list element points to a list of all
  elements with the same name in the same document

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XISS - Element Index
element list
did list
nid
element list
ltorder, sizegt,Depth,ParentID
B-tree
element record
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XISS - Attribute Index

• Very similar to element index
• always has a value identifier, vid

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XISS - Structure Index

• Input did, Output array containing all the
  element and attributes in the document
• implemented by a B-tree

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XISS - Structure Index
did
nidltorder, sizegt,Parent order,Child
order,Sibling order,Attribute order
B-tree
record array
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XISS - Indices

• When to use which index?
• first use Name Index to find nid of the
  element/attribute to be queried
• search Element/Attribute index for the records
• if we need values, lookup Value Table
• use Structure Index to rebuild or traverse the
  XML document tree

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XISS - Join Algorithms

• After getting the record lists from each
  subexpression, we need to find out which are
  answers to the original query
• e.g., to find /A/B, we found a record list of all
  element A, another list of all element B, and we
  have to find out which Bs are A/B

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XISS - Join Algorithms

• Three join algorithms proposed
• EA-join - merges an element record list and an
  attribute record list (solves A/_at_B)
• EE-join - merges two element record lists (solves
  A/B or A//B)
• KC-join - self-merge an element record list
  (solves (E))

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XISS - EA-Join

• to solve E/_at_A
• input an element record list and an attribute
  record list
• find out the attribute records which have parents
  in the element record list
• two lists are sorted by did and then order

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XISS - EA-join

• 2-stage sort-merge
• group by did first
• merge using order then
• output criterion E is a parent of A
• single scan on both list is enough

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XISS - EE-join

• to solve E/_/E, e.g., E/E, E//E, E/_/E
• input two Element record lists, E, F
• output (e,f) where e is an ancestor of f
• also use 2-stage sort-merge
• however, may need scanning of lists multiple
  times (for special cases, e.g., the document has
  /A/A/B/B)

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XISS - KC-join

• to solve Kleene Closure of a subexpression
• input a list of element records fits the base
  case
• recursively use EE join on the list, and stop
  until no more grow in the result list

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Index Fabric

• by Cooper at el, published in VLDB 2001, with
  title A fast index for semistructured data
• has 2 subtypes, raw path index and refined path
  index
• use Patricia technique to compress the index

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Index Fabric - General Idea

• it is a disk balanced indexing structure based on
  Patricia
• each data node is associated with a key string
  and this string is stored in the trie index for
  retrieval
• the layered approach in building the index ensure
  the number of disk pages accessed per query

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Index Fabric - General Idea

• raw path index answers absolute path queries
• refined path index answers any predefined queries
• the difference is how to generate the key

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Patricia

• Patricia Practical Algorithm To Retrieve
  Information Coded in Alphanumeric
• by Morrison, in JACM 1968
• a method to store and retrieve strings in a
  space efficient way
• binary, use bit comparisons, has a skip in each
  internal node

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Patricia

• an example Patricia trie

0
1
0
0
1
1
101110
101111
110000
110011
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Patricia

• its basically a trie with internal nodes having
  single child removed
• search is done by
• branch according to the value of bit at skip
• retrieve the string at leaf
• compare it with the query string

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Index Fabric - Balanced Trie

• The number of disk pages accessed per query is
  bounded by the number of layers in the layered
  index
• The idea is similar to that of B-tree, The
  Patricia trie is decomposed into blocks, and
  there is an upper layer trie which traverse the
  blocks

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Index Fabric - Balanced Trie
1

• e.g.

0
1
0
0
1
1
101110
101111
110000
110011
Layer 0
Layer 1
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Index Fabric - Balanced Trie

• There are 3 types of links in the balanced trie
• far link across layer, a result of branching
• near link within the same block, a result of
  branching
• direct link across layer, the root nodes are the
  same
• Each query will access 1 block in 1 layer

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Index Fabric - Balanced Trie

• increase the speed by skipping nodes of original
  trie using traversals in upper layers
• number of page accessed is bounded

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Index Fabric - Raw Path

• each data node is associated with a key
• key path (encoded in designators) value
• designators are special characters, each
  represents a name
• APE queries are translated to prefix to keys and
  submitted to the index trie

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Index Fabric - Raw Path

• Example
• ltinvoicegtltbuyergtltnamegtHKUlt/namegtlt/buyergtlt/invoice
  gt is translated to IBNHKU (bolded underlined
  are designators
• query of /invoice/buyer/nameHKU is translated
  to query string IBNHKU

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Index Fabric - Refined Path

• Special designators can be assigned to special
  queries (can be regular)
• e.g., we define P as the path //buyer/name, and
  PHKU means there is a buyer/name has value HKU in
  the document
• can answer any predefined RPE very quickly

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Comparison

• XISS
• can solve general RPE
• solve APE by dividing it into steps

• Index Fabric
• RPE solved by compile time expansion of RPE or
  using predefined Refined Path Index
• solve APE by single index lookup