Parallel algorithms for finding connected components using linear algebra

Parallel Algorithms for Connected Components

In this paper, we describe our implementation of several parallel graph algorithms for nding connected components. Our implementation, with virtual processing, is on a 16,384-processor MasPar MP-1 using the language MPL. We present extensive test data on our code. In our previous projects [21, 22, 23], we reported the implementation of an extensible parallel graph algorithms library. We develop...

Parallel Algorithms for Detecting Strongly Connected Components

Connected components algorithms for mesh-connected parallel computers

We present a new CREW PRAM algorithm for nding connected components. For a graphG with n vertices andm edges, algorithmA0 requires at mostO(logn) parallel steps and performsO((n+m) logn) work in the worst case. The advantage our algorithm has over others in the literature is that it can be adapted to a 2-D mesh-connected communication model in which all CREW operations are replaced byO(logn) pa...

Parallel algorithms in linear algebra

This paper provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues, we consider the problem of parallel solution of a nonsingular linear system by Gaussian elimination with partial pivoting. This problem has come to be regarded...

Optimal Algorithms for Finding Connected Components of an Unknown Graph

We want to nd the connected components of an unknown graph G with a known vertex set V. We learn about G by sending an oracle a query set S V , and the oracle tells us the vertices connected to S. We want to use the minimum number of queries, adaptively, to nd the components. The problem is also known as interconnect diagnosis of wiring networks in VLSI. The graph has n vertices and k component...