Optimal Search Strategy for Finding Transients in Large-sky Error Regions under Realistic Constraints

In order to identify the rapidly fading, optical transient counterparts of gravitational-wave (GW) sources, an efficient follow-up strategy is required. Since most ground-based optical telescopes aimed at following up GW sources have a small field of view (FOV) as compared to the GW sky error region, we focus on a search strategy that involves dividing the GW patch into tiles of the same area as the telescope FOV to strategically image the entire patch. We present an improvement over the optimal algorithm outlined in Rana et al. by factoring in the effects of air mass, telescope slew, and setting constraints into the scheduling algorithm in order to increase the chances of identifying the GW counterpart. We propose two separate algorithms: the air-mass-weighted algorithm, a solution to the Hungarian algorithm that maximizes probability acquired while minimizing the image air mass, and the slew-optimization algorithm that minimizes the overall slew angle within the observation schedule using the traveling salesman algorithm. We simulate hundreds of telescope-patch configurations to test the performance of our algorithms. Our results indicate that slew optimization can reduce the cumulative slew angle by hundreds of degrees, saving minutes of observation time without any loss of probability. Further, we demonstrate that, as compared to the greedy algorithm, the air-mass-weighted algorithm can acquire up to 20% more probability and 30 deg^2 more in areal coverage for skymaps of all sizes and configurations. Our analysis can be straightforwardly extended to optical counterparts of gamma-ray bursts, as well as to other telescopes or sites