Constant Time Graph and Poset Algorithms on the Reconfigurable Multiple Bus Machine

Abstract

The Reconfigurable Multiple Bus Machine (RMBM) is a model of parallel computation based on reconfigurable buses. In this paper, vie present constant time RMBM algorithms for a collection of basic, graph problems that include, lowest common ancestors and Euler tour related problems (for trees) and shortest path and connectivity re lated problems (for general graphs). We also present re sults for some poset and lattice problems. All algorithms are at least as efficient or more efficient in terms of pro cessors than corresponding PARBUS algorithms.

Constant Time Graph Algorithms on the Reconfigurable Multiple Bus Machine

“…Also, in a fiber optic implementation, buses are inherently directional [21]. The directional RMBM has found use in the context of directed graphs [28]; Ben-Asher et al [4] and Ercal and Lee [6] also used related directional models.…”

On the Power of Segmenting and Fusing Buses

“…For example, an RMBM can rank a list of n elements in constant time with n 1ϩ processors (for any constant Ͼ 0) [25,28], while the best R-Mesh algorithm for the same problem uses ⌰(n 2ϩ ) processors [19]. Also, a (2n Ϫ 2) processor RMBM can compute an Euler tour of an n vertex tree in constant time [27,28], while the R-Mesh uses n 2 processors for the same problem [13]. As a third example, an RMBM with ⌰(n 2ϩ ) processors (for any constant Ͼ 0) can find the connected components of an n vertex graph in constant time [27]; the best R-Mesh solution for this problem uses ⌰(n 4 ) processors [34].…”

“…Also, a (2n Ϫ 2) processor RMBM can compute an Euler tour of an n vertex tree in constant time [27,28], while the R-Mesh uses n 2 processors for the same problem [13]. As a third example, an RMBM with ⌰(n 2ϩ ) processors (for any constant Ͼ 0) can find the connected components of an n vertex graph in constant time [27]; the best R-Mesh solution for this problem uses ⌰(n 4 ) processors [34]. In each of these cases, the RMBM uses switches to manipulate buses where the R-Mesh would have to use processors for the same purpose.…”

“…The reconfigurable multiple bus machine (RMBM) [25][26][27]] is a recent model that has some advantages over the RN and other graph-based reconfigurable models. The RMBM distinguishes between processors and switches, so it can be used to design algorithms that are more processorefficient than their RN counterparts that use many processors only as switches.…”

“…Other reconfigurable bus-based models include the bus automation [17], reconfigurable array processor (RAP) [8] and reconfigurable buses with shift switching (REBSIS) [14]. Recently, the authors have proposed the Reconfigurable Multiple Bus Machine (RMBM) [25][26][27]. Sahni has proposed an extension to the RMBM called the distribution memory bus computer (DMBC) [21,22].…”