Recently, Mamba-based frameworks have achieved substantial advancements across diverse computer vision and NLP tasks, particularly in their capacity for reasoning over long-range information with linear complexity. However, the fixed 2D-to-1D scanning pattern overlooks the local structures of an image, limiting its effectiveness in aggregating 2D spatial information. While stacking additional Mamba layers can partially address this issue, it increases parameter intensity and constrains real-time application. In this work, we reconsider the local optimal scanning path in Mamba, enhancing the rigid and uniform 1D scan through the local shortest path theory, thus creating a structure-aware Mamba suited for lightweight single-image super-resolution. Specifically, we draw inspiration from the Traveling Salesman Problem (TSP) to establish a local optimal scanning path for improved structural 2D information utilization. Here, local patch aggregation occurs in a content-adaptive manner with minimal propagation cost. TSP-Mamba demonstrates substantial improvements over existing Mamba-based and Transformer-based architectures. For example, TSP-Mamba surpasses MambaIR by up to 0.7dB in lightweight SISR, with comparable parameters and very slightly extra computational demands (1-2 GFlops for 720P images).