Maximum incomplete recursive circulants in graph embeddings

Abstract

An incomplete recursive circulant possesses virtually every advantage of a complete recursive circulant, including simple deadlock-free routing, a small diameter, a good support of parallel algorithms, and so on. It is natural to reconfigure a faulty recursive circulant into a maximum incomplete recursive circulant so as to lower potential performance degradation. For [Formula: see text], the maximum incomplete subgraph problem is to identify a subgraph [Formula: see text] of a graph [Formula: see text] on [Formula: see text] vertices having the maximum number of edges among all subgraphs on [Formula: see text] vertices and is NP-complete. In this paper we identify maximum incomplete recursive circulants and use them as a tool to compute the exact wirelength of embedding recursive circulants into special classes of trees, such as [Formula: see text]-rooted complete binary trees, [Formula: see text]-rooted sibling trees, binomial trees, certain caterpillars and path.