Using Bus Linearization to Scale the Reconfigurable Mesh

Recently, many parallel computing models using dynamically reconfigurable electrical buses have been proposed in the literature. The underlying characteristics are similar among these models, but they do have certain differences that can take form of restrictions on configurations allowed. This paper presents a constant time simulation of an R-Mesh on an LR-Mesh (a restricted model of the R-Mesh), proving that in spite of the differences, the two models possess the same complexity. In other words, the LR-Mesh can simulate a step of the R-Mesh in constant time with a polynomial increase in size. This simulation is based on Reingold's algorithm to solve USTCON in log-space. The simulation is also the first to be executed in constant time.

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“…We can accomplish this task by using a procedure similar to the one presented in [2]. It is possible to embed graph…”

Section: Algorithm 3 Ustcon On An Lr-meshmentioning

confidence: 99%

“…Fernández-Zepeda et al [2] demonstrated, using the bus linearization technique, that an LR-Mesh of N × N processors can simulate an R-Mesh of the same size in O(log N ) time. This simulation is optimal in the number of processors, and before this paper, it was the fastest simulation of this type.…”

Section: Introductionmentioning

confidence: 99%

Constant Time Simulation of an R-Mesh on an LR-Mesh

Córdova-Flores¹,

Fernández-Zepeda²,

Bourgeois

2007

2007 IEEE International Parallel and Distributed Processing Symposium

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“…For example, they efficiently solve problems such as sorting [19,21], selection [3,7], arithmetic operations [5,17], graph problems [8,11], geometric problems [9,14,15,18], image processing [1,2,4], self simulation [6]. See [20] for the comprehensive survey.…”

Section: Figure 3 An Example Of Subbusesmentioning

confidence: 99%

Randomized Initialization on the 1-Dimensional Reconfigurable Mesh

Sánchez‐Gómez

Youlou

2007

Eighth International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT 2007)

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The reconfigurable mesh is a processor array that consists processors arranged in 1-dimensional or 2dimensional grids with a reconfigurable bus system. The main contribution of this paper is to show initialization algorithms on the 1-dimensional reconfigurable mesh with Ò processors. We assume that processors are identical, and does not have unique IDs. Initialization is a task that assigns sequential IDs to processors in the reconfigurable mesh. We first show a simple deterministic initialization algorithm for the 1-dimensional reconfigurable mesh that runs in Ç´Òµ time. This deterministic algorithm is optimal, because no deterministic solution can perform initialization in less than Ç´Òµ time. Quite surprisingly, we show that expected sublinear-time initialization is possible if we use randomized techniques. Our initialization algorithm runs in Ç´´ÐÓ Ò· Ð Ó µ ÐÓ ÐÓ Òµ time with probability at least ½ ½ for every real number ½. It follows that the initialization algorithm runs in expected Ç´ÐÓ Ò ÐÓ ÐÓ Òµ time.We also proved that any randomized initialization need to run in ª´ÐÓ Òµ time. Thus, our randomized initialization algorithm running in Ç´ÐÓ Ò ÐÓ ÐÓ Òµ time is very close to a theoretical lower bound ª´ÐÓ Òµ time.

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

Matsumae¹

2006

Journal of Parallel and Distributed Computing

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Using Bus Linearization to Scale the Reconfigurable Mesh

Cited by 13 publications

References 30 publications

Constant Time Simulation of an R-Mesh on an LR-Mesh

Constant Time Simulation of an R-Mesh on an LR-Mesh

Randomized Initialization on the 1-Dimensional Reconfigurable Mesh

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

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