## 1 Introduction  
The concept of Simultaneous Localization and Mapping (SLAM) [1] emerged as a fundamental problem in mobile robotics, initially addressed by probabilistic methods such as EKF-SLAM [2], FastSLAM [3], and Graph-SLAM [4], which used Kalman filters and graphs for trajectory and map estimation. In the last decade (2015 to 2025), the number of publications related to SLAM per year has increased by 292.7% [5], reflecting growing interest and advancements in the field. With advances in computing, visual approaches such as ORB-SLAM [6], LSD-SLAM [7], and DSO [8] improved real-time pose estimation. In the context of autonomous driving, sensor fusion has become essential for handling dynamic environments, leading to the development of methods such as LIO-SAM [9] and VINS-Mono [10], which integrate LiDAR and IMU data to enhance localization accuracy. Recently, the state of the art in SLAM has incorporated deep-learning-based techniques, such as DeepVO [11] and CodeSLAM [12], which leverage neural networks to learn compact environment representations and improve the robustness of visual odometry. Additionally, innovative approaches like NeRF-SLAM [13], 3D Gaussian Splitting [14], and NICE-SLAM [15] explore implicit representations to enhance high-fidelity 3D scene reconstruction. Hybrid methods such as R3 LIVE [16] and NeRF-LOAM [17] combine the advantages of classical and modern techniques to overcome challenges in unstructured environments and variable lighting conditions. The integration of SLAM with Large Language Models (LLMs) [18] and semantic perception systems, such as SuMa++ [19] and SemanticKITTI [20], has demonstrated advancements in understanding complex scenes. In the current landscape, approaches like DL-SLOT [21] and LIO-SEGMOT [22] incorporate multi-object tracking to handle dynamic obstacles, while ClusterSLAM [23] and TwistSLAM [24] improve odometry accuracy in dense urban scenarios. These advancements show SLAM evolving to meet autonomous vehicle demands. Despite these advancements, one of the key challenges in SLAM remains ensuring the completeness of the generated maps. SLAM allows robots to map and localize simultaneously. This capability is crucial for applications ranging from autonomous vehicles [25] to space exploration [26]. Ensuring full coverage, especially in dynamic scenarios, remains a challenge. Traditional SLAM approaches often rely on random or exploratory navigation methods that, although capable of covering most of the environment, lack efficient mechanisms to systematically explore unmapped regions [1]. This leads to shadowed areas, redundant paths, and map gaps [27, 28]. Industrial robots need efficient mapping for logistics and safety. In search-and-rescue, full coverage is vital for finding survivors. The ability to accurately detect and close unexplored areas makes MARS-SLAM particularly suitable for these domains, where incomplete maps could lead to inefficiencies or critical mission failures. Moreover, conventional methods lack a deterministic process to verify mapping completion, often resulting in unnecessary exploration that wastes time, energy, and computational resources. To address these challenges, this research proposes MARS-SLAM, a novel approach that enhances mapping completeness through the use of virtual markers placed in unexplored regions. These markers, derived from LiDAR sensor readings, dynamically guide the robot's exploration, ensuring systematic coverage while optimizing resource usage. The key contributions of this study are:  
1. A marker-based methodology for identifying and tracking unexplored areas, enabling a structured exploration process that minimizes redundant revisits. 2. An adaptive navigation strategy that prioritizes markers based on their distance and antiquity, improving mapping efficiency. 3. An optimized path-finding system that enhances navigation efficiency when direct access to a target marker is obstructed. 4.