Budget Amount *help 
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1999 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1998 : ¥2,200,000 (Direct Cost : ¥2,200,000)

Research Abstract 
We constructed a fixed routing model in which faulttolerance of optical networks can be evaluated and we obtain the following results in the model. 1. The surviving route graph R(G,ρ)/F for a graph G, a routing p and a set of faults F is a directed graph consisting of nonfaulty nodes with a directed edge from a node x to a node y if there are no faults on the route from x to y. The diameter of the surviving route graph (denoted by D(R(G,ρ)/F) could be one of the faulttolerance measures for the graph G and the routine p. We show that we can construct a routing for any triconnected planar graph with a triangle such that a diameter of the surviving route graphs is two (thus optimal) for any faults F(F【less than or equal】 2). We also show that we can construct a routing λ for every nnode kconnected graph such that n 【greater than or equal】 2kィイD12ィエD1, in which the route degree is O(kィイD8nィエD8), the total number of routes is O(kィイD12ィエD1n)DA and D(R(G,λ)/F) 【less than or equal】 3 for
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any fault set F(F < k) and we can construct a routing ρィイD21ィエD2 for every nnode biconnected graphs, in which the total number of routes is O(n) and D(R(G,ρィイD21ィエD2)/{f}) 【less than or equal】 2 for any fault f, and using ρィイD21ィエD2 a routing ρィイD22ィエD2 for every nnode biconnected graphs, in which the route degree is O(ィイD8nィエD8), the total number of routes is O(nィイD8nィエD8) and D(R(G,ρィイD22ィエD2)/{f}) 【less than or equal】 2 for any fault f. 2. We describes efficient algorithms for partitioning a Kedgeconnected graph into k edgedisjoint connected subgraphs, each of which has a special number of elements (vertices and edges). If each subgraph contains the specified element (called base), we call this problem the mixed kpartition problem with bases (called kPARTWB), otherwise we call it the mixed kpartition problem without bases (called kPARTWOB). This partition problems can be used to define optimal faulttolerant routings. We show that kPARTWB always has a solution for every kedgeconnected graph and we consider the problem without bases and we obtain the following results : (1) for any k 【greater than or equal】 2, kPARTWOB can be solved in O(VィイD8VlogィイD22ィエD2BVィエD8+E) time for every 4edgeconnected graph G = (V, E), (2) 3PARTWOB can be solved in O(VィイD12ィエD1) for every 2edgeconnected graph G = (V,E) and (3) 4PARTWOB can be solved in O(EィイD12ィエD1) for every 3edgeconnected graph G = (V,E). We also show that if the input graph is planar, all the kpartition problems stated above can be solved in linear time. Less
