An Efficient Algorithm for Positioning Tiles in the Sloan Digital Sky Survey

The Sloan Digital Sky Survey (SDSS) will observe around 10⁶ spectra from targets distributed over an area of about 10, 000 square degrees, using a multi-object fiber spectrograph which can simultaneously observe 640 objects in a circular field-of-view (referred to as a ``tile'') 1. 49 degrees in radius. No two fibers can be placed closer than 55'' during the same observation; multiple targets closer than this distance are said to ``collide. '' We present here a method of allocating fibers to desired targets given a set of tile centers which includes the effects of collisions and which is nearly optimally efficient and uniform. Because of large-scale structure in the galaxy distribution (which form the bulk of the SDSS targets), a naive covering the sky with equally-spaced tiles does not yield uniform sampling. Thus, we present a heuristic for perturbing the centers of the tiles from the equally-spaced distribution which provides more uniform completeness. For the SDSS sample, we can attain a sampling rate greater than 92% for all targets, and greater than 99% for the set of targets which do not collide with each other, with an efficiency greater than 90% (defined as the fraction of available fibers assigned to targets).