Constant Time Graph Algorithms on the Reconfigurable Multiple Bus Machine

On the Power of Segmenting and Fusing Buses

“…Part (i) is a well-known fact (for instance, see [7,9,10]). Part (ii) follows from a result in [27,28] …”

“…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. 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].…”

“…We now describe a technique called ''neighbor localization'' (see also [28,29,31]) that finds use in subsequent discussion. Consider a set of P processors.…”

“…This effectively places the write port of a processor to the right of the read port. The data movement required for this is quite straightforward; details appear in [28].…”

“…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].…”