Community detection is a common task in network analysis that provides insights into the structural organization of large-scale complex systems. Real-world networks, such as social, biological, and web networks, often contain billions of nodes and edges. There is a need for a fast community detection algorithm that gives communities of reasonably high quality and is capable of processing large-scale networks quickly. Among the existing community detection algorithms, the label propagation algorithm (LPA) is widely used due to its simplicity, speed, and ability to yield reasonably good communities. Some recent work has focused on improving its runtime. A recent algorithm, the fast label propagation algorithm (FLPA, 2023), achieves a substantial runtime improvement over the basic LPA. We present the heap-based label propagation algorithm (HLPA), which is faster than FLPA and leads to better parallelization. Based on HLPA, we present the parallel heap-based label propagation algorithm (PHLPA) for shared-memory systems. Rigorous experiments on eight networks of varying sizes (up to 1.8 billion edges) and domains demonstrate that our HLPA and PHLPA algorithms are faster than state-of-the-art sequential and parallel algorithms, respectively. As a result, HLPA and PHLPA are fast, efficient, and scalable algorithms for community detection in large-scale complex networks.