Indra Rajasingh

Exact wirelength of hypercubes on a grid

Grid embeddings are used not only to study the simulation capabilities of a parallel architecture but also to design its VLSI layout. In addition to dilation and congestion, wirelength is an important measure of an embedding. There are very few papers in the literature which provide the exact wirelength of grid embedding. As far as the most versatile architecture hypercube is concerned, only approximate estimates of the wirelength of grid embedding are available. In this paper, we give an exact formula of minimum wirelength of hypercube layout into grids and thereby we solve completely the wirelength problem of hypercubes into grids. We introduce a new technique to estimate the wirelength of a grid embedding. This new technique is based on a Congestion Lemma and a Partition Lemma which we study in this paper.

On minimum metric dimension of honeycomb networks

A minimum metric basis is a minimum set W of vertices of a graph G(V,E) such that for every pair of vertices u and v of G, there exists a vertex [emailxa0protected]?W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. The honeycomb and hexagonal networks are popular mesh-derived parallel architectures. Using the duality of these networks we determine minimum metric bases for hexagonal and honeycomb networks.

An efficient representation of Benes networks and its applications

The most popular bounded-degree derivative network of the hypercube is the butterfly network. The Benes network consists of back-to-back butterflies. There exist a number of topological representations that are used to describe butterfly-like architectures. We identify a new topological representation of butterfly and Benes networks. The minimum metric dimension problem is to find a minimum set of vertices of a graph G(V,E) such that for every pair of vertices u and v of G, there exists a vertex w with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. It is NP-hard in the general sense. We show that it remains NP-hard for bipartite graphs. The algorithmic complexity status of this NP-hard problem is not known for butterfly and Benes networks, which are subclasses of bipartite graphs. By using the proposed new representations, we solve the minimum metric dimension problem for butterfly and Benes networks. The minimum metric dimension problem is important in areas such as robot navigation in space applications.

Embedding of cycles and wheels into arbitrary trees

We estimate and characterize the edge congestion-sum measure for embeddings of various graphs such as cycles, wheels, and generalized wheels into arbitrary trees. All embedding algorithms apply an interesting general technique based on the consecutive label property. Our algorithms produce optimal values of sum of dilations and sum of edge-congestions in linear time.

Embedding hypercubes into cylinders, snakes and caterpillars for minimizing wirelength

We consider the problem of embedding hypercubes into cylinders to minimize the wirelength. Further, we show that the edge isoperimetric problem solves the wirelength problem of regular graphs and, in particular, hypercubes into triangular snakes and caterpillars.

Embeddings of circulant networks

In this paper we solve the edge isoperimetric problem for circulant networks and consider the problem of embedding circulant networks into various graphs such as arbitrary trees, cycles, certain multicyclic graphs and ladders to yield the minimum wirelength.

Landmarks in torus networks

Abstract A minimum metric basis is a minimum set M of vertices of a graph G(V, E) such that for every pair of vertices u and v of VM, there exists a vertex w∈M with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. In this paper we study the minimum metric dimension problem for torus networks. We prove that for torus TR(m, n), m≤n, the minimum metric dimension is 3 when at least one of m or n is odd. We provide an upper bound for the minimum metric dimension when both m and n are even.

Embedding of special classes of circulant networks, hypercubes and generalized Petersen graphs

Hypercubes are a very popular model for parallel computation because of their regularity and the relatively small number of interprocessor connections. In this paper, we present an algorithm for embedding special class of circulant networks into their optimal hypercubes with dilation 2 and prove its correctness. Also, we embed special class of circulant networks into special class of generalized Petersen graphs with dilation 2 and vice versa.

Embedding of hypercubes into necklace, windmill and snake graphs

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. In this paper, we determine the exact wirelength of embedding hypercubes into necklace, windmill and snake graphs.

Linear Wirelength of Folded Hypercubes

Manuel etxa0al. (Discret. Appl. Math. 157(7):1486–1495, 2009) obtained the exact wirelength of an r-dimensional hypercube into a path as well as a