A network flow algorithm to position tiles for LAMOST

Abstract

We introduce the network flow algorithm used by the Sloan Digital Sky Survey (SDSS) into the sky survey of the Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) to position tiles. Because fibers in LAMOST's focal plane are distributed uniformly, we cannot use SDSS' method directly. To solve this problem, firstly we divide the sky into many small blocks, and we also assume that all the targets that are in the same block have the same position, which is the center of the block. Secondly, we give a value to limit the number of the targets that the LAMOST focal plane can collect in one square degree so that it cannot collect too many targets in one small block. Thirdly, because the network flow algorithm used in this paper is a bipartite network, we do not use the general solution algorithm that was used by SDSS. Instead, we give our new faster solution method for this special network. Compared with the Convergent Mean Shift Algorithm, the network flow algorithm can decrease observation times with improved mean imaging quality. This algorithm also has a very fast running speed. It can distribute millions of targets in a few minutes using a common personal computer.