The twisted crossed cube

Abstract

SUMMARYThe topology of interconnection networks plays an important role in the performance of parallel and distributed computing systems. In this paper, we propose a new interconnection network called twisted crossed cube (TCQ n ) and investigate its basic network properties in terms of the regularity, connectivity, fault tolerance, recursiveness, hamiltonicity and ability to simulate other architectures, and so on. Then, we develop an effective routing algorithm Route (u, v) for TCQ n that takes no more than d(u, v) + 1 steps for any two nodes (u, v) to communicate with each other, and the routing process shows that the diameter, wide diameter, and fault-tolerant diameter of TCQ n are about half of the corresponding diameters of the equivalent hypercube with the same dimension. In the end, by combining TCQ n with crossed cube (CQ n ), we propose a preferable dynamic network structure, that is, the dynamic crossed cube, which has the same network diameter as TCQ n /CQ n and better properties in other respects, for example, its connection complexity is half of that of TCQ n /CQ n when the network scale is large enough, and the number of its average routing steps is also much smaller than that in TCQ n /CQ n .

Set-to-Set Disjoint Path Routing in Bijective Connection Graphs

“…degree n, including the twisted cube [3], the crossed cube [4], the Möbius cube [5], the locally twisted cube [6], the spined cube [7], and the twisted crossed cube [8]. Hence, such algorithms are enthusiastically studied [9]- [13].…”

Minimal Paths in a Bicube

“…There are many previous works regarding the twisted cube [17], [18]. An n-dimensional twisted crossed cube has a diameter ⌈(n + 1)/2⌉ [7]. It is not nodeor edge-symmetric.…”

“…. , t 0 ) = (1, 1, 1, 0, 1, 0, 0)) induces P = {s (7) , s (5) , s (4) , s (3) , s (2) , s (1) , s (0) }. Because u 6 = 0, MPRE(s, t) returns P. For each node in P, there is a minimal path that includes the node such as s → s (7) = (1, 0, 0, 0, 1, 1, 0, 0) → s (7,5) = (1, 0, 1, 0, 1, 1, 0, 0) → s (7,5,4) = (1, 0, 1, 1, 1, 1, 0, 0) → s (7,5,4,3) = (1, 0, 1, 1, 0, 1, 0, 0)(= t), s → s (5) = (0, 0, 1, 0, 1, 1, 0, 0) → s (5,4) = (0, 0, 1, 1, 1, 1, 0, 0) → s (5,4,7) = (1, 0, 1, 1, 1, 1, 0, 0) → s (5,4,7,3) = (1, 0, 1, 1, 0, 1, 0, 0)(= t), s → s (0) = (0, 0, 0, 0, 1, 1, 0, 1) → s (0,7) = (1, 0, 1, 1, 0, 0, 1, 0) → s (0,7,2) = (1, 0, 1, 1, 0, 1, 1, 0) → s (0,7,2,1) = (1, 0, 1, 1, 0, 1, 0, 0)(= t), and so on.…”

Implementing Exchanged Hypercube Communication Patterns on Ring-Connected WDM Optical Networks

“…For future research, it would be worthwhile to consider the routing and wavelength problem for other types of communication patterns, such as twisted crossed cubes [27], exchanged folded hypercubes [28], exchanged crossed cubes [29] and locally twisted cubes [30]. It will also be promising to investigate other WDM optical network topologies, such as linear array, meshes, and torus, and to consider the routing and wavelength problem by using the dynamic wavelength assignment strategy [13], [16].…”