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### 5.4 Multi-Object Matches

The matching in TOPCAT is determined by specified match criteria, as described in Appendix A.8.1.1. These criteria give conditions for whether two items (table rows) count as matched with each other. In the case of a pair match, it is clear how this is to be interpreted.

However, some of the matching operations such as the Internal Match search for match groups which may have more than two members. This section explains how TOPCAT applies the pair-wise matching criteria it is given to identifying multi-object groups.

In a multi-object match context, the matcher identifies a matched group as the largest possible group of objects in which each is linked by a pair match to any other object in the group - it is a group of "friends of friends". Formally, the set of matched groups is a set of disjoint graphs whose nodes are input table rows and whose edges are successful pair matches, where no successful pair match exists between nodes in different elements of that set. Thus the set has a minimal number of elements, and each of its elements is a matched group of maximal size. The important point to note is that for any particular pair in a matched group, there is no guarantee that the two objects match each other, only that you can hop from one to the other via pairs which do match.

So in the case of a multi-object sky match on a field which is very crowded compared to the specified error radius, it is quite possible for all the objects in the input table(s) to end up as part of the same large matching group. Results at or near this percolation threshold are (a) probably not useful and (b) likely to take a long time to run. Some care should therefore be exercised when specifying match criteria in multi-object match contexts.

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TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk