Efficient Routing and Broadcasting Algorithms in de Bruijn Networks

Abstract

Recently, routing on dBG has been investigated as shortest path and fault tolerant routing but investigation into shortest path in failure mode on dBG has been non-existent. Furthermore, dBG based broadcasting has been studied as local broadcasting and arc-disjoint spanning trees based broadcasting. However, their broadcasting algorithms can only work in dBG(2,k). In this paper, we investigate shortest path routing algorithms in the condition of existing failure, based on the Bidirectional de Bruijn graph (BdBG). And we also investigate broadcasting in BdBG for a degree greater than or equal to two 1 .

Computational Aspects of Carbon and Boron Nanotubes

“…The broadcasting problem is NP-complete for 3-regular planar graphs and a constant deadline k ≥ 2 [ 27 ]. This problem is studied almost on all kinds of architectures and systems for example, wireless sensor networks [ 28 ], cellular networks of triangular systems [ 29 ], heterogeneous tree networks [ 30 ], honeycomb networks [ 31 ], higher dimensional hexagonal networks [ 32 ], mesh architectures [ 33 ], star graphs [ 34 ], de Bruijn Networks [ 35 ], hypercubes [ 36 ].…”

Optimal routing algorithms for Hyper-de Bruijn networks

“…1 shows us an example for BdBG (2,4). It's obviously to obtain links from a node (xm-lXm-2 ... XO Y n-l Y n-2 ... Y O) to the following nodes (in deBruijn part):…”

“…Corollary 1: path ending in RLR or LRL cannot be shortest path ( shift string ending in 101 or 010 cannot represents a shortest path) [2].…”

“…Corollary 2: shortest path must be in the form Rx, Ly, RmLn, LmRn, RmLnRp, or LmRnLp except cases provided by theorem 6 and 7 [2]. Step 2.…”