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Physically-based illumination is an essential factor for realistic rendering. In this context, hierarchical radiosity is one of the most accurate global illumination methods. One of the key features of the radiosity approach is that it obtains view-independent global illumination results. Unfortunately, global illumination has high computational and memory requirements, and hierarchical radiosity, though more efficient than other radiosity solutions, is not an exception. The progressive popularization of multiprocessor and multi-core processor systems makes the design and implementation of efficient parallel algorithms an appealing alternative in this field. In this paper we present a novel parallel radiosity method addressing the hierarchical radiosity computation on current homogeneous multi-core environments. One of the main contributions of our work is the use of different tasks to exploit the independent interactions among the geometric elements in the scene. Our parallel solution leads to a versatile radiosity implementation that takes advantage of the multiple computational resources in the system, such as multi-core processors and SMT (simultaneous multithreading) capabilities. Good results in terms of performance have been achieved.