The notion of optimality of a parallel algorithm is closely tied to the characteristics of the parallel machine. A parallel implementation of radiosity solution is chosen for studying relationship between algorithms and parallel architectures. The radiosity method determines a view independent solution to scene illumination. This approach is computationally intensive and can benefit from parallelism. An algorithm for solving the radiosity equation was previously developed for Intel iPSC/2, a tightly coupled message passing multiprocessor. This algorithm when directly ported to IBM RS6000 LAN performed worse than a serial algorithm due to the high message latency of a LAN. Network parameters on the LAN multicomputer were measured. A new algorithm that minimizes the number of messages by increasing task granularity is proposed. The results obtained using this algorithm indicated expected performance improvements.>