Optimal Asynchronous Rendezvous for Mobile Robots with Lights

We study a Rendezvous problem for 2 autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible when robots have no lights in basic common models, even if the system is semi-synchronous. On the other hand, Rendezvous is possible if robots have lights with a constant number of colors in several types lights. In asynchronous settings, Rendezvous can be solved by robots with 4 colors of lights in non-rigid movement, if robots can use not only own light but also other robot's light (full-light), where non-rigid movement means robots may be stopped before reaching the computed destination but can move a minimum distance \delta > 0 and rigid movement means robots can reach the computed destination. In semi-synchronous settings, Rendezvous can be solved with 2 colors of full-lights in non-rigid movement. In this paper, we show that in asynchronous settings, Rendezvous can be solved with 2 colors of full-lights in rigid movement and in non-rigid movement if robots know the value of the minimum distance \delta. We also show that Rendezvous can be solved with 2 colors of full-lights in general non-rigid movement if we consider some reasonable restricted class of asynchronous settings.