# Matcher Design Notes

This document is incomplete at present. It lacks explanation of the min-heap used to keep the best N M-set items (Managing Gigabytes describes this technique well), the check() method isn't discussed, and probably some other things.

# The PostList Tree

The QueryOptimiser class builds a tree structure of PostList objects from the query. At the leaf level, a PostList object is created for each term, and for other leaf-level subqueries, like PostingSource objects and value ranges. Then pairs or groups of PostLists are combined using 2-way or n-way branching tree elements for AND, OR, etc - these are virtual PostLists whose class names reflect the operation (MultiAndPostList, OrPostList, etc). See below for a full list.

## OR

For a group of OR operations, each OrPostList has two children, job). The OR tree is built up in a similar way to how an optimal huffman code is constructed, so the sub-PostLists with the fewest entries are furthest down the tree, and those with most nearest the top (this is more efficient than an n-ary tree in terms of the number of comparisons which need to be performed, ignoring various optimisations which the matcher can perform - it may actually be the case that a MultiOrPostList could do a better job in practice though).

OR is coded for maximum efficiency when the right branch has fewer postings in than the left branch.

When an OR gets "at end", it autoprunes, replacing itself with the branch that still has postings - see below for full details.

## AND

For a multi-way AND operation, we have MultiAndPostList, which tries the sub-postlists in order from least frequent to most frequent (two-way AND is handled the same way). This will generally minimise the number of posting list entries we read and maximises the size of each skip_to.

When one of a sub-trees of AND operations runs out, the sub-query will signal "at end", and this causes the AND to signal "at end" too.

The OP_FILTER query operator is actually treated as AND in the postlist tree - the boolean-ness is pushed down to the leaf query, where it is handled by the Weight object.

## Other operations

The other operations also handle "at end" either like OR or AND (for asymmetric operations like AND_MAYBE, which happens may depend which branch has run out).

# running the match

Once the tree is built, the matcher repeatedly asks the root of the tree for the next matching document and compares it to those in the proto-mset it maintains. Once the proto-mset is of the desired final size, the candidate needs to score more highly that the lowest scoring document in the proto-mset (either by weight, or in sort order if sorting is used) to be interesting. If it is, the lowest scoring document is removed (which is easy as we store the proto-mset as a min heap) and the candidate is added.

When the matcher itself gets "at end" from the postlist tree, the match process ends.

The matcher also passes the lowest weight currently needed make the proto-mset into the tree, and each node may adjust this weight and pass it on to its subtrees. Each PostList can report a minimum weight it could contribute - so if the left branch of an AND will always return a weight of 2 or more, then if the whole AND needs to return at least 6, the right branch is told it needs to return at least 4.

For example, an OR knows that if its left branch can contribute at most a weight of 4 and its right branch at most 7, then if the minimum weight is 8, only documents matching both branches are now of interest so it mutates into an AND. If the minimum weight is 6 it changes into an AND_MAYBE (A AND_MAYBE B matches documents which which match A, but B contributes to the weight - in most search engines query syntax, that's expressed as +A B). See the "Operator Decay" section below for full details of these mutations. If the minimum weight needed is 12, no document is good enough, and the OR returns "end of list".

# Phrase and near matching

The way phrase and near matching works is to perform an AND query for all the terms, with a filter node in front which only returns documents whose positional information fulfils the phrase requirements.

Because checking the positional information can be quite costly compared to matching postlist trees, we hoist the position check higher up the tree in cases when the phrase operation is below an AND. So A AND (B NEAR C) will actually filter the results of (A AND B AND C) through a check for B NEAR C, which means we never need to check positions for documents which don't match A.

# virtual postlist types

There are several types of virtual PostList. Each type can be treated as boolean or probabilistic - the only difference is whether the weights are ignored or not. The types are:

- OrPostList: returns documents which match either branch
- MultiAndPostList: returns documents which match all branches
- MultiXorPostList: returns documents which match an odd number of branches
- AndNotPostList: returns documents which match the left branch, but not the right (the weights of documents from the right branch are ignored).
- AndMaybePostList: returns documents which match the left branch - weights from documents also in the right branch are added in for the probabilistic case ("X ANDMAYBE Y" is what Altavista did for "+X Y").
- FIXME: this list is no longer complete...

[Note: You can use AndNotPostList to apply an inverted boolean filter to a probabilistic query]

There are two main optimisations which the best match performs: autoprune and operator decay.

# autoprune

For example, if a branch in the match tree is "A OR B", when A runs out then "A OR B" is replaced by "B". Similar reductions occur for XOR, ANDNOT, and ANDMAYBE (if the right branch runs out). Other operators (AND, FILTER, and ANDMAYBE (when the left branch runs out) simply return "at_end" and this is dealt with somewhere further up the tree as appropriate.

An autoprune is indicated by the next or skip_to method returning a pointer to the PostList object to replace the postlist being read with.

# operator decay

The matcher tracks the minimum weight needed for a document to make it into the m-set (this decreases monotonically as the m-set forms). This can be used to replace on boolean operator with a stricter one. E.g. consider A OR B - when maxweight(A) < minweight and maxweight(B) < minweight then only documents matching both A and B can make it into the m-set so we can replace the OR with an AND. Operator decay is flagged using the same mechanism as autoprune, by returning the replacement operator from next or skip_to.

Possible decays:

- OR → AND
- OR → ANDMAYBE
- ANDMAYBE → AND
- XOR → ANDNOT

A related optimisation is that the Match object may terminate early if maxweight for the whole tree is less than the smallest weight in the mset.