Contention free embedding of complete binary trees into 3D meshes in half and full-duplexed network models

We consider the problem of dimension-ordered embedding of complete binary trees into 3-dimensional meshes without link contention. In this paper, the embedding problems are studied under two different network models: half-duplexed networks and full-duplexed networks. Gibbons and Paterson showed that a complete binary tree T_p could be disjointedly embedded into a full-duplexed 2-dimensional mesh of optimum size without dimension-ordered routing. Using the dimension-ordered routing, the authors showed that T_p could be embedded into a 3-dimensional mesh of optimum size with link congestion two. This paper presents the dimension-ordered embedding algorithms of the complete binary trees into the wormhole routed 3-dimensional meshes without link contention achieving expansion of no larger than 1.125 of optimum in half-duplexed network model and optimum in full-duplexed network model