发表机构
Tsinghua University; IIIS（清华大学; 交叉信息研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对六度三角网格与环面，提出仅禁两个转向的单/双虚拟通道最小无死锁路由，并支持单链路故障的三角旁路，保持全对连通性。
AI 中文摘要
六度三角网格互连网络提供了大量的最短路径多样性，但其额外的方向在虫孔流控下使无死锁路由复杂化。我们在一个共同的六方向坐标系中研究有限六边形网格及其周期环面商。对于有限网格，我们构造了一个最小部分自适应路由关系，该关系使用一个虚拟通道且仅禁止两个有向转向。对于环面，我们证明了每个源-目的对具有唯一的最接近晶格提升，但相同的两转向物理路由关系对于每个n≥3仍具有循环的单虚拟通道资源通道依赖图。我们通过将两个虚拟通道与哈密顿坐标和组特定日期线相结合来消除这种残余的周期依赖。每个同组段最多跨越其日期线一次，这允许对带虚拟通道标签的通道资源进行全局排序。我们证明了两种物理路由关系的最小全对连通性，以及所提出的单虚拟通道网格和双虚拟通道环面构造的完整资源通道依赖图的无环性。对于在路由时段之前已知的单个静态双向链路故障，我们进一步将转向规则向故障方向旋转，并将故障跳替换为同组两跳三角旁路。这种受限扩展保持了全对连通性和原始虚拟通道数量，相对于健康最短路径距离最多增加一跳。
英文摘要
Degree-six triangular-lattice interconnection networks offer substantial minimal-path diversity, but their additional directions complicate deadlock-free routing under wormhole flow control. We study a finite hexagon-shaped mesh and its periodic torus quotient in a common six-direction coordinate system. For the finite mesh, we construct a minimal partially adaptive routing relation that uses one virtual channel and forbids only two directed turns. For the torus, we prove that every source-destination pair has a unique closest lattice lift, but that the same two-turn physical routing relation still has a cyclic one-VC resource CDG for every n >= 3. We eliminate this residual periodic dependency by combining two virtual channels with Hamiltonian coordinates and group-specific datelines. Each same-group segment crosses its dateline at most once, which permits a global rank on VC-labelled channel resources. We prove minimal all-pairs connectivity for both physical routing relations and acyclicity of the complete resource CDG for the proposed one-VC mesh and two-VC torus constructions. For a single static bidirectional link failure known before a routing epoch, we further rotate the turn rule toward the failed orientation and replace a failed hop by a same-group two-hop triangle bypass. This restricted extension preserves all-pairs connectivity and the original VC counts, with at most one additional hop relative to the healthy shortest-path distance.
Comments25 pages, 8 figures, 7 tables, including appendices
