| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1988: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1987: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Research Abstract |
We investigated design problems of 3-dimentional VLSI circuits from various theoretical points of view, and clarified difficulities underlying the problems. Furtherm ore we designed routing algorithms, implemented prototypes of practical routing programs, and then theoretically analyzed their performance. We now briefly describe the obtained results.
1. The single-layer routing problem of VLSI circuits can be formulated as a problem of finding Steiner forests in planar (grid) graphs G. Given a planar graph G representing a routing regiona and set of nets, we wish to find a Steiner forest, hat is, disjoint trees each interconnecting all the terminals of a net. We obtained a very efficient algorithm to solve this problem for the case all the terminals lie on two specified faces. The algorithm runs in O(MIN{kn,n log n}) time if G has n vertices and there are k terminals.
2. We obtained an O(n log n ) algorithm to find internally-disjoint paths in planar graphs. Using a divide-and conquer approach, this algorithm first determines the maximum number k of internally-disjoint paths connecting two specified vertices, and then actually finds k paths in a given graph. This is used by the algorithm above.
3. We gave an efficient algorithm to find edge-disjoint paths in grid graphs surrounded by two nested rectangles.
4. We newly define the fg-edge-coloring of graphs, and established an upper bound on the fg-chromatic index. Furthermore we designed an approximation algorithm of fg-coloring graphs, which is useful for some of scheduling problems.
5. We obtained an O(m^2) algorithm which divides a given 3-connected graph into three connected induced subgraphs of specified sizes, where n denotes the number of vertices in a graph.
6. We designed a multi-layer channel routing algorithm for 3-dimentional VLSI circuits, and analyzed its performance and computation time. furtherm ore we implemented it into a prototype of a practical routing program for 3-dimentional VLSI circuits.
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