The concept of tracking overlaps differently at different scales in a hierarchical manner is what I was trying to get at.

My idea was that at each scale one could compute overlapping scales for effective radii on the scale of that HEALpix level. E.g., for a level of effective resolution 1 degree, record the matches for galaxies with effective radii of that scale, e.g. LMC, SMC, and Andromeda (which is not in LSST's footprint). Then at the next level down, say 30' arcminutes, record the nearest galaxy for galaxies with effective radii on scales of 30 arcminutes. Then at the 10" level you will only record the nearest galaxies with effective radii on the scales of 10".

There's some factor between the HEALpix resolution and the range of effective radii one wants to explore and maybe some detail about the shape of pixels.

I agree that HEALpix is an implementation detail, any hierarchical mapping would be fine.

Thank you Michael Wood-Vasey for the clarification and my apologies for not catching on to the full scope of your suggestion. I've added a subsection to DMTN-151 under "Recommendations" to elaborate on this option (pasted below) and am going to make a comment on it in the RFC to inspire further discussion on which option should be pursued.

\subsection{Option: Hierarchical Association}

Instead of associating a {\tt DIAObject} with the three extended {\tt Objects} with the lowest separation distance, associate with the three nearest neighbors at three size scales. For example, the nearest $R_e<10"$ neighbor within $d<100"$ (high-$z$ and small galaxies), the nearest $R_e<100"$ neighbor within $d<1000"$ (large low-$z$ galaxies), and the nearest $R_e<1000"$ neighbor within $d<10000"$ (very large nearby galaxies). In this option, the ``nearest neighbor" would be the extended {\tt Object} with the lowest separation distance, as calculated from, e.g., the second moments (Section \ref{ssec:options_mom}).

However, this option does not avoid the issue of contamination by background galaxies as discussed in Appendix \ref{sec:appB}. To mitigate background interlopers, the nearest \emph{three} extended sources for each size scale should be included. This might seem unnecessary for the largest size scale but it would assist with identifying transients in galaxy groups and clusters, especially the rare transients with large offsets which might belong to intracluster stellar populations.

This option would add unit64[9] and float[9] to the {\tt DIAObject} catalog and to each alert, instead of unit64[3] and float[3]. However, it would also vastly reduce the number of extended {\tt Objects} that are considered during the host association process, and would impose a lower computational load. Since 9 potential associations are reported instead of 3, this option would also lower the probability of the failure scenario (in which the true host galaxy is not associated with the {\tt DIAObject}) and increase the amount of contextual information passed in the alert, which would benefit science applications.

Updated RFC-695 and DMTN-151 with a simplified proposal.

Posted to Community.lsst.org to seek feedback.

There was one response from the community about the proposal to update the host association parameters was received, and it is favorable: https://community.lsst.org/t/host-galaxy-association-for-lsst-transients-request-for-comments/4812

Adopting RFC-695, implementation in https://jira.lsstcorp.org/browse/DM-29731

This ticket is Done.