Constructing Independent Spanning Trees on Generalized Recursive Circulant Graphs

Abstract

The generalized recursive circulant networking can be widely used in the design and implementation of interconnection networks. It consists of a series of processors, each is connected through bidirectional, point-to-point communication channels to different neighbors. In this work, we apply the shortest path routing concept to build independent spanning trees on the generalized recursive circulant graphs. The proposed strategy loosen the restricted conditions in previous research and extended the result to a more general vertex setting by design the specific algorithm to deal with the constraint issue.

Ring-Split: Deadlock-Free Routing Algorithm for Circulant Networks-on-Chip

“…A simpler implementation, the clockwise routing algorithm developed for use in ring-type circulants, does not guarantee optimal routes. In addition to the routing algorithms mentioned in [ 17 ], there are many different implementations of routing algorithms developed at different times by a number of authors for different classes of circulant networks [ 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. The existing algorithms for routing in circulant topologies have both advantages and disadvantages and can be used depending on the task.…”

A parallel algorithm for constructing multiple independent spanning trees in bubble-sort networks

“…From then on, this conjecture has been confirmed only for k-connected graphs with k ≤ 4 (see [9,10,14]). Since this conjecture is still unsolved for general k-connected graphs for k ≥ 5, the follow-up research mainly focused on the study of constructing ISTs on specific interconnection networks, e.g., the construction of ISTs on some variations of hypercubes [3,20,29,30,37], torus networks [28], recursive circulant graphs [34,35], and special subclasses of Cayley networks [7,8,12,13,15,19,39]. In particular, special topics related to ISTs include the research on reducing the height of the ISTs [31,33,36] and parallel construction of ISTs [4-6, 32, 37, 38].…”