在 VLSI 设计中,多点互连是物理设计阶段的关键问题之一,而互连的点数等于 2 或大于 2 分别对应于

Manhattan 空间上有障碍时的最短路径问题和最小 Steiner 树问题,显然前者是后者的基础.连接图是研究最短路径

问题的有效工具,已有的典型连接图包括基于轨迹的GC 和GT 以及基于自由区的GF 和GG.工作包括3个方面:设计并分析了在各种连接图上实现动态的点对之间的最短路径查询算法 分析了在各个连接图上构造 3-Steiner 树的算

法,对于已有的 GC 上的 3-Steiner 算法,将其 Steiner 顶点的候选集合规模从 O((e+p)

2

)降低到了 O((t+p)

2

),其中 e,t,p

分别表示边数、障碍极边数和顶点数 设计了在GG上的3-Steiner树构造算法,其平均情况时间复杂度只有Θ(t). -Abstract:　 Finding networks with minimal cost　to connect points　is a key problem in VLSI design, which can be

described as obstacle-avoiding shortest path and minimum Steiner tree problem according to whether the number of

points is greater than 2. Connection graphs, such as track based on graphs GC　 and GT　 and free area based graphs

GF and GG, are effective　tools　for the　shortest path problem, which is the　foundation of the Steiner tree problem.

The contribution of this paper includes three points: The dynamic algorithms for querying the shortest path between

two　points on　each connection graph are designed and analyzed for the first time　 secondly, all algorithms for

Steiner　problem on each connection graph are analyzed　The　number of candidate Steiner points is reduced　from

O((e+p)

2

) to O((t+p)

2

) in the 3-Steiner algorithm on GC, where e, t, p presents the number of edges, extreme edges

of obstacles and terminals　An average Θ(t) algorithm for