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The use of regex potentially results in full table scans (as each node's xpath needs to be compared against the regex), severely impacting performance, and causing query time duration to grow linearly with the fragment table size (i.e. queries get slower as the database gets bigger).

Path queries using path-component lookup

A new solution is being proposed where each path component of the Cps Path is looked up in constant time, thus addressing performance issues.

Objective of the proposed solution

The objective is to achieve the maximum performance for queries.

• For a query that will return 1 out of N items, the best theoretical time complexity is constant, O(1). The existing solution is linear, O(N).
• For a query that will return all N items, the best theoretical time complexity is linear, O(N). The existing solution is quadratic, O(N²).

Implementation Proposal

The new approach involves adding a column to the Fragment table, storing the last path component (called xpath_component here). The new column is indexed, to allow constant-time lookups.

In addition, the mechanism for fetching descendant nodes returned from the query causes worst case quadratic performance.

Why does the existing solution have worst case quadratic complexity?

The reason the existing solution is quadratic time when fetching descendants is because the path query translates into a number of SQL queries:

1. An SQL query that returns nodes matching query criteria - O(N)
2. For each node returned from query 1, another SQL query is issued to fetch that node with descendants, using a LIKE operator - O(N).

The LIKE operator has linear time complexity, as all nodes' xpaths in a given anchor need to be examined.

In the case of a query that matches all N nodes, we are issuing 1+N queries, each with complexity O(N). Thus the overall complexity is O(N²).

Path queries using path-component lookup

A new solution is being proposed where each path component of the Cps Path is looked up in constant time, thus addressing performance issues.

Objective of the proposed solution

The objective is to achieve the maximum performance for queries.

• For a query that will return 1 out of N items, the best possible time complexity is constant, O(1).
• For a query that will return all N items, the best possible time complexity is linear, O(N).

Implementation Proposal

The new approach involves adding a column to the Fragment table, storing the last path component (called xpath_component here). The new column is indexed, to allow constant-time lookups.

...

SELECT
    * 
FROM
    fragment 
WHERE
    parent_id IN (
        SELECT
            id 
        FROM
            fragment 
        WHERE
            xpath_component = 'categories[@code=''1'']'
            AND parent_id = (
                SELECT
                    id 
                FROM
                    fragment 
                WHERE
                    xpath_component = 'bookstore'
                    AND anchor_id = 3
                    AND parent_id IS NULL
            )
        ) 
        AND (
            xpath_component = 'books'
            OR xpath_component LIKE 'books[%'
        ) 
        AND (
            attributes @> '{"title":"Matilda"}'
        )

Comparison with existing solution

Given the following (incomplete) fragment table:

In addition, a new algorithm for fetching descendants is implemented.

Recursive SQL query to fetch descendants

The proposed solution will use recursive SQL to fetch descendants of fragment returned from the CPS path query:

WITH RECURSIVE descendant_search AS (
  SELECT id, 0 AS depth
    FROM fragment
   WHERE id IN (:fragmentIds)
   UNION
  SELECT child.id, depth + 1
    FROM fragment child INNER JOIN descendant_search ds ON child.parent_id = ds.id
   WHERE depth <= :maxDepth
) 
SELECT f.id, anchor_id AS anchorId, xpath, f.parent_id AS parentId, CAST(attributes AS TEXT) AS attributes 
FROM fragment f INNER JOIN descendant_search ds ON f.id = ds.id

Comparison with existing solution

Given the following (incomplete) fragment table:

...

...

...

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A note on fetching descendant nodes

The above sections only partly describe the current and proposed solutions. In the existing solution, a CPS path query is actually sent as multiple database queries:

1. The first SQL query performs the CPS path query.
2. Additional SQL queries fetch the descendant nodes, if required.
   • Alternatively, if an ancestor CPS path was provided, the second SQL query would fetch the ancestors (and their descendants if required).

Recursive SQL query to fetch descendants

The proposed solution will use recursive SQL to fetch descendants of fragment returned from the CPS path query:

...

...

Here is a visualization of both algorithms, executing a query for /bookstore/categories[@code='1']/books[@title='Matilda']:

Proof of Concept

A proof of concept (poc) implementation was developed so that performance could be compared against existing Cps Path query algorithms.

...

...

Why does the existing solution have worst case quadratic complexity?

The reason the existing solution is quadratic time when fetching descendants is because the path query translates into a number of SQL queries:

1. An SQL query that returns nodes matching query criteria - O(N)
2. For each node returned from query 1, another SQL query is issued to fetch that node with descendants, using a LIKE operator - O(N).

The LIKE operator has linear time complexity, as all nodes' xpaths in a given anchor need to be examined.

...

Possible improvements of proposed solution

Cps Path Query capabilities can be

...

extended

Presently, Cps Path queries limit leaf-condition, text-condition, etc. to the final path component. The proposed solution allows for future improvement where conditions could be applied to any or all path components.

...

The main algorithm was mostly done during the PoC (all integration tests are passing for the PoC). The existing PoC code can thus be refactored to make it production ready.

It may be possible to incorporate the recursive SQL descendant search into the existing solution as a starting point.

DB upgrade

Because a new column is being added to the Fragment table, this column needs to be populated. An SQL script will be needed to provide a value for of the new xpath_component field based on existing xpath field.

...