Online algorithm for exploring a grid polygon with two robots.

This paper considers the problem of exploring an unknown grid polygon with two robots. Assume that the robot has limited sensing capability that can only detect four basic cells adjacent to it. The goal of them is to visit each cell and return to the start. They can communicate with each other during the exploration. We are interested in the strategy that can minimizing the number of multiple-visit cells. We use competitive ratio to measure the performance of the strategy. It is the ratio between the length of the online exploration tour and the length of the shortest offline exploration tour. We propose a 1.8 competitive strategy for this problem and prove that the lower bound is 1.125.