Tight bounds on the simulation of meshes with dynamically reconfigurable row/column buses by meshes with statically partitioned buses

Matsumae, Susumu

doi:10.1016/j.jpdc.2006.04.008

Cited by 4 publications

(7 citation statements)

References 11 publications

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“…Lemma 1 [5,6] In this section, we show that we obtain the almost same result as Lemma 1, even if we assume that L is non-constant.…”

Section: A Simulation Of the Word-model Msb By The Word-model Mmpbsupporting

confidence: 54%

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

Matsumae¹

2012

IJACSA

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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 ...

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“…Lemma 1 [5,6] In this section, we show that we obtain the almost same result as Lemma 1, even if we assume that L is non-constant.…”

Section: A Simulation Of the Word-model Msb By The Word-model Mmpbsupporting

confidence: 54%

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

Matsumae¹

2012

IJACSA

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“…Because of the broadcasting capability, the MB can solve the prefix-sum problem more efficiently in O ( n 1/2 ) time steps [16]. The mesh with partitioned buses (MPB) is a variant of the MB model, where each broadcasting bus is equally partitioned by a fixed length ℓ [2,6] ) steps [11]. To obtain more powerful computational power, dynamically reconfigurable broadcasting buses have been studied [18].…”

Section: Modelsmentioning

confidence: 99%

Impact of Reconfigurable Function on Meshes with Row/Column Buses

Matsumae

2011

IJNC

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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 mesh-connected computer with dynamically reconfigurable row/column buses. The broadcasting buses of the MSB can be dynamically sectioned into smaller bus segments by program control. We examine the impact of reconfigurable capability on the computational power of the MSB model, and investigate how computing power of the MSB decreases when we deprive the MSB of its reconfigurability. We show that any single step of the MSB of size n × n can be simulated in O (log n) time by the MSB without its reconfigurable function, which means that the MSB of size n × n can work with O (log n) step slowdown even if its dynamic reconfigurable function is disabled.

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“…By combining the following 2 algorithms (thick arrows in Fig. 3 ), we can say that our scaling-simulation algorithm [11] is optimal when m = O(n 1-ε ) for ε > 1/6. Here in this paper, we further improve the cost toward O(n/m (n/m + log m)).…”

Section: Scaling-simulationmentioning

confidence: 99%

Effective Partitioning of Static Global Buses for Small Processor Arrays

Matsumae

2011

Journal of Information Processing Systems

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Abstract-This paper shows an effective partitioning of static global row/column buses for tightly coupled 2D mesh-connected small processor arrays ("mesh", for short). With additional O(n/m (n/m + log m)) time slowdown, it enables the mesh of size m×m with static row/column buses to simulate the mesh of the larger size n×n with reconfigurable row/column buses (m ≤ n). This means that if a problem can be solved in O(T) time by the mesh of size n×n with reconfigurable buses, then the same problem can be solved in O(T n/m (n/m + log m)) time on the mesh of a smaller size m×m without a reconfigurable function. This time-cost is optimal when the relation n ≥ m log m holds (e.g., m = n 1-ε for ε > 0).

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Tight bounds on the simulation of meshes with dynamically reconfigurable row/column buses by meshes with statically partitioned buses

Cited by 4 publications

References 11 publications

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

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

Impact of Reconfigurable Function on Meshes with Row/Column Buses

Effective Partitioning of Static Global Buses for Small Processor Arrays

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