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Simulation Algorithms among Enhanced Mesh Models
Susumu MATSUMAE Nobuki TOKURA
IEICE TRANSACTIONS on Information and Systems
Publication Date: 1999/10/25
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Algorithm and Computational Complexity
parallel algorithm, simulation, reconfigurable mesh, mesh with multiple broadcasting, connected component labeling,
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In this paper, we present simulation algorithms among enhanced mesh models. The enhanced mesh models here include reconfigurable mesh and mesh with multiple broadcasting. A reconfigurable mesh (RM) is a processor array that consists of processors arranged to a 2-dimensional grid with a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns among the processors during the execution of programs. A horizontal-vertical RM (HV-RM) is obtained from the general RM model, by restricting the network topology it can take to the ones in which each bus segment must be along row or column. A mesh with multiple broadcasting (MWMB) is an enhanced mesh, which has additional broadcasting buses endowed to every row and column. We present two algorithms:1) an algorithm that simulates a HV-RM of size nn time-optimally in θ(n) time on a MWMB of size nn, and 2) an algorithm that simulates a RM of size nn in θ(log2 n) time on a HV-RM of size nn. Both algorithms use a constant number of storage in each processor. Furthermore, we show that a RM of size nn can be simulated in θ((n/m)2 log n log m) time on a HV-RM of size mm, in θ ((n/m)2 m log n log m) time on a MWMB of size mm (m < n). These simulations use θ((n/m)2) storage in each processor, which is optimal.