T. M. Rajalaxmi

Bothway embedding of circulant network into grid

Graph embedding is an important technique that maps a guest graph into a host graph, usually an interconnection network. In this paper, we compute the dilation and wirelength of embedding circulant network into grid and vice versa.

A Tight Bound for Congestion of an Embedding

Graph embedding has been known as a powerful tool for implementation of parallel algorithms or simulation of different interconnection networks. Congestion is one of the main optimization objectives in global routing. In this paper, we introduce a technique to obtain a tight bound for congestion of an embedding. Moreover, we give algorithms to compute exact congestion of embedding the hypercubes into the cylinder and the torus and prove that the bound obtained is sharp.

Embedding of Recursive Circulants into Certain Necklace Graphs

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. Interconnection networks provide an effective mechanism for exchanging data between processors in a parallel computing system. In this paper, we embed recursive circulants into certain necklace graphs for minimizing the wirelength.

Maximum incomplete recursive circulants in graph embeddings

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 k > 2, the maximum incomplete subgraph problem is to identify a subgraph H of a graph G on k vertices having the maximum number of edges among all subgraphs on k 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 k-rooted complete binary trees, k-rooted sibling trees, binomial trees, certain caterpillars and path.

Embedding Circulant Networks into Butterfly and Benes Networks

The dilation of an embedding is defined as the maximum distance between pairs of vertices of host graph that are images of adjacent vertices of guest graph. An embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise. In this paper, we compute the minimum dilation of embedding circulant networks into butterfly and benes networks.