We propose a dual-resolution scheme to achieve time-efficient autonomous exploration with one or many robots. The scheme maintains a high-resolution local map of the robot's immediate vicinity and a low-resolution global map of the remaining areas of the environment. We believe that the strength of our approach lies in this low- and high-resolution representation of the environment: The high-resolution local map ensures that the robots observe the entire region in detail, and because the local map is bounded, so is the computation burden to process it. The low-resolution global map directs the robot to explore the broad space and only requires lightweight computation and low bandwidth to communicate among the robots. This paper shows the strength of this approach for both single-robot and multirobot exploration. For multirobot exploration, we also introduce a "pursuit" strategy for sharing information among robots with limited communication. This strategy directs the robots to opportunistically approach each other. We found that the scheme could produce exploration paths with a bounded difference in length compared with the theoretical shortest paths. Empirically, for single-robot exploration, our method produced 80% higher time efficiency with 50% lower computational runtimes than state-of-the-art methods in more than 300 simulation and real-world experiments. For multirobot exploration, our pursuit strategy demonstrated higher exploration time efficiency than conventional strategies in more than 3400 simulation runs with up to 20 robots. Last, we discuss how our method was deployed in the DARPA Subterranean Challenge and demonstrated the fastest and most complete exploration among all teams.