## 可重組態架構上之有向圖平行演算法 Parallel Digraph Algorithms on Reconfigurable Architectures

2011

Tien-Tai, Pan
##### Abstract

Reconfigurable architectures have attracted many researchers and scientists for their high performance computing for the past three decades. They are very powerful parallel computation models, but some types of problems have not been studied completely, for example, the digraph problems. The directional reconfigurable architectures are developed especially for digraph problems, they are idealistic machines for handling such problems. In this dissertation, we focus on digraph problems by using non-directional reconfigurable architectures and try to solve them by a new approach. Before this study, to our best knowledge, there are two approaches to solve digraph problems on reconfigurable architectures. The first one is on the basis of matrix multiplication which is independent of computation models. It was used to solve the algebraic path problems (APP), for example, transitive closure (TC), all-pairs shortest path (APSP), the minimum spanning tree (MST), on non-directional reconfigurable architectures. The second approach uses directional reconfigurable architectures, such as directional reconfigurable mesh (DR-Mesh) and complete directional processor arrays with reconfigurable bus systems (CD-PARBS), to solve specified digraph problems. The algorithms of the second approach specifically use the capability of the directional reconfigurable architectures which can control the data flow in each segment of a bus. In this dissertation, the third approach on non-directional reconfigurable architectures will be proposed to solve many digraph problems. For example, the transitive closure problem can be solved in $O(log \,d(D))$ time on a three-dimensional (3-D) $n\!\times\!n\!\times\!n$ reconfigurable mesh (R-Mesh), where $d(D)$ is the diameter of digraph $D$. Based on the same idea used in the transitive closure algorithm, we can solve the following digraph problems: strongly connected graph, strongly connected component (SCC), cyclic digraph checking, tree construction, all-pairs shortest distance, single source shortest distance, diameter, topological sort (TS). These algorithms show the power of the third approach. So we believe this approach is valuable to digraph problems on non-reconfigurable architectures for the high performance computing and time-critical applications.