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Exploration and mapping of unknown environments is a fundamental task in applications for autonomous robots. In this article, we present a complete framework for deploying MAVs in autonomous exploration missions in unknown subterranean areas. The main motive of exploration algorithms is to depict the next best frontier for the robot such that new ground can be covered in a fast, safe yet efficient manner. The proposed framework uses a novel frontier selection method that also contributes to the safe navigation of autonomous robots in obstructed areas such as subterranean caves, mines, and urban areas. The framework presented in this work bifurcates the exploration problem in local and global exploration. The proposed exploration framework is also adaptable according to computational resources available onboard the robot which means the trade-off between the speed of exploration and the quality of the map can be made. Such capability allows the proposed framework to be deployed in a subterranean exploration, mapping as well as in fast search and rescue scenarios. The overall system is considered a low-complexity and baseline solution for navigation and object localization in tunnel-like environments. The performance of the proposed framework is evaluated in detailed simulation studies with comparisons made against a high-level exploration-planning framework developed for the DARPA Sub-T challenge as it will be presented in this article.