Cluster Finder

We begin by finding clusters, groups of contiguous (or nearly contiguous) two-packs of the same orientation¹ in a single panel which all register signals in the event.

The algorithm for finding clusters is as follows:

1.

loop over all hits in the event;

2.

look at all existing clusters with the same arm, plane, panel, and orientation as the hit;

• if the hit is not ``close enough'' to any existing cluster, create a new cluster containing the hit.
• if the hit is ``close enough'' to an existing cluster, add the hit to the cluster.
• if the hit is ``close enough'' to two existing clusters, merge the two clusters: add the hit - and all hits in the second cluster - to the first cluster, then remove the second cluster.

The criterion for a hit to be ``close enough'' to a cluster is determined by a parameter called the cluster gap. The cluster gap is the maximum size of any set of contiguous non-firing two-packs allowed to be contained within the cluster boundaries.² A cluster gap of zero requires that the cluster contain a contiguous set of firing two-packs, while nonzero cluster gaps allow larger clusters with missing two-packs. Table 1 shows the clusters obtained from an example hit pattern for various gap parameters.

Table 1: Cluster-finder results for various cluster-gap parameters. We consider two-packs of a single orientation in a single panel; two-packs 21, 23, 24, and 26 have signals in the event.

Cluster Gap	Identifiers of two-packs in
	first cluster	second cluster	third cluster
0	21	23 24	26
1	21 23 24	26	-
2	21 23 24 26	-	-

We use a cluster gap of zero to simplify matters for the current road finder. This choice reduces (but does not eliminate) the possibility of extraneous hits being associated with a cluster and shifting the cluster centroid position; in such cases, otherwise-good roads that include that cluster are often lost, because the projection of the road trajectory to the vertex plane deviates from the expected value.