### Optimal Routing Algorithm in Multilayer Octagon-Cell: A New Class of Octagon-Cell Interconnected Networks

Sanjukta Mohanty, Prafulla Kumar Behera
2017 Transactions on Networks and Communications
In communication system of network routing algorithm acts an important role. The efficiency of a parallel system depends on the reliable and efficient routing algorithm which is used to route the messages between the fault-free nodes. In this paper a new class of interconnection network of Octagon-Cell is introduced, which is called Multilayer Octagon-Cell (MLO). The structure of Multilayer Octagon-cell is recursive in nature. It can be expanded, if we increase the depth of MLO. This paper
more » ... duces the node degree, diameter, number of links, bisection width of the MLO network and we have also developed the optimal routing algorithm of MLO. Each level i has Ni nodes, representing processing elements and interconnected in a ring structure. In an octagon-cell network, the number of nodes at level i is: Ni = 8(4i-3) Now at level 1, N1 = 8, since there is a single octagon-cell with 8 vertices. Level 2 introduces 8 octagoncells. Therefore at level 2 the number of nodes N2 = 8(4*2-3) = 8*5 = 40, N3 = 8(4*3-3) = 8*9 = 72 In octagon-cell the level (i+1) has 32 nodes in addition to corresponding nodes to those at level i. Therefore Ni = 8 + (i-1)*32 = 8+32*i-32 = 32*i-24 = 8(4*i-3) The total number of nodes in an octagon-cell network is, Or we can write N = 8i (2i-1), Now N = 16d 2 -8d or 16d 2 = N+8d or d 2 = N+8d/16 or d = 1/4 √( + 8 ) Therefore the total no of nodes at level 1 is N = 8(2*1-1) = 8 At level 2, N = 8(2*4-2) = 48 At level 3, N = 8(2*9-3) = 120 and so on. Figure 2: Addressing nodes in Octagon-Cell with level:2 T r a n s a c t i o n s o n N e t w o r k s a n d C o m m u n i c a t i o n s ; V o l u m e 5 , I s s u e 1 , F e b r u a r y 2 0 1 7 C o p y r i g h t © S o c i e t y f o r S c i e n c e a n d E d u c a t i o n U n i t e d K i n g d o m 3 3 Multilayer Octagon-Cell Interconnection Network Number of Nodes Multilayer Octagon-Cell (MLO) is a modular interconnection network which consists of layers of identical Octagon-Cell networks connected together in a hierarchical order. The MLO is represented as MLO (k, d), where k denotes the layer number and d denotes the depth of the identical Octagon-Cell. Each Layer k has Ni nodes, where Ni = 8kd (2d-1).