Polylogarithmic Gap between Meshes with Reconfigurable Row/Column Buses and Meshes with Statically Partitioned Buses

Abstract

Abstract-This paper studies the difference in computational power between the mesh-connected parallel computers equipped with dynamically reconfigurable bus systems and those with static ones. The mesh with separable buses (MSB) is the meshconnected parallel computer with dynamically reconfigurable row/column buses. The broadcast buses of the MSB can be dynamically sectioned into smaller bus segments by program control. We show that the MSB of size can work with ( ) step even if its dynamic reconfigurable function is disabled. Here, we assume the word-model broadcast buses, and use the relation between the word-model bus and the bit-model bus.Keywords-mesh-connected parallel computer; dynamically reconfigurable bus; statically partitioned bus; simulation algorithm. I.INTRODUCTIONThe mesh-connected parallel computers equipped with dynamically reconfigurable bus systems gained much attention due to their strong computational powers [3,11,12,13,14]. The dynamic reconfigurable function enables the models to make efficient use of broadcast buses, and to solve many important, fundamental problems efficiently, mostly in a constant or polylogarithmic time [13]. Such reconfigurability, however, makes the bus systems complex and causes negative effects on the communication latency of global buses [2]. Hence, it is practically important to study the trade-off between such points quantitatively.In this paper, we investigate the impact of reconfigurable capability on the computational power of mesh-connected computers with global buses. Here, we deal with the meshes with separable buses (MSB) [3,12] and a variant of the meshes with partitioned buses called the meshes with multiple partitioned buses (MMPB) [4]. The MSB and the MMPB are the mesh-connected computers enhanced by the addition of broadcast buses along every row and column.The broadcast buses of the MSB, called separable buses, can be dynamically sectioned into smaller bus segments by program control, while those of the MMPB, called partitioned buses, are statically partitioned in advance and cannot be dynamically reconfigurable. In the MSB model, each row/column has only one separable bus, while in the MMPB model, each row/column has partitioned buses ( ). By comparing the relative power between these models, we clarify the difference in computational power between the parallel models equipped with reconfigurable bus systems and those with static ones. In this paper, we assume that the size of MSB and that of MMPB are of . The case of different sizes was investigated in [8].Here, we study how much slowdown is necessary when we deprive the MSB of its reconfigurable function. In [5,6], we have shown that the MSB of size can be simulated timeoptimally in ( ⁄ ) steps using the MMPB of size , where L is constant and the global buses are of word-model, i.e., the bus-width is the same as the number of bits in one word. From this result, it is natural to think that the slowdown may be at least of polynomial time. However, here we show that we can suppress the slowdown to ...