<p><b>Abstract</b>—Mesh-connected computers (MCCs) are a class of important parallel architectures due to their simple and regular interconnections. However, their performances are restricted by their large diameters. Various augmenting mechanisms have been proposed to enhance the communication efficiency of MCCs. One major approach is to add nonconfigurable buses for improved broadcasting. A typical example is the mesh-connected computer with multiple buses (MMB). We propose a new class of generalized MMBs, the improved generalized MMBs (IMMBs). We compare IMMBs with MMBs and a class of previously proposed generalized MMBs (GMMBs). We show the power of IMMBs by considering semigroup and prefix computations. Specifically, as our main result we show that for any constant <tmath>$0 < \epsilon < 1$</tmath>, one can construct an <tmath>$N^{{1 \over 2}} \times N^{1 \over 2}$</tmath> square IMMB using which semigroup and prefix computations on <tmath>$N$</tmath> operands can be carried out in <tmath>$O(N^{\epsilon})$</tmath> time, while maintaining <tmath>$O(1)$</tmath> broadcasting time. Compared with the previous best complexities <tmath>$O(N^{ 1\over {8}})$</tmath> and <tmath>$O(N^{1\over {16}})$</tmath> achieved on a rectangular MMB and GMMB, respectively, for the same computations, our results show that IMMBs are more powerful than MMBs and GMMBs.</p>