Hong-Chun Hsu

A class of hierarchical graphs as topologies for interconnection networks

We study some topological and algorithmic properties of a recently defined hierarchical interconnection network, the hierarchical crossed cube HCC(k,n), which draws upon constructions used within the well-known hypercube and also the crossed cube. In particular, we study: the construction of shortest paths between arbitrary vertices in HCC(k,n); the connectivity of HCC(k,n); and one-to-all broadcasts in parallel machines whose underlying topology is HCC(k,n) (with both one-port and multi-port store-and-forward models of communication). Moreover, some of our proofs are applicable not just to hierarchical crossed cubes but to hierarchical interconnection networks formed by replacing crossed cubes with other families of interconnection networks. As such, we provide a generic construction with accompanying generic results relating to some topological and algorithmic properties of a wide range of hierarchical interconnection networks

A fast fault-identification algorithm for bijective connection graphs using the PMC model

Diagnosis of reliability is an important topic for interconnection networks. Under the classical PMC model, Dahura and Masson [5] proposed a polynomial time algorithm with time complexity O(N^2^.^5) to identify all faulty nodes in an N-node network. This paper addresses the fault diagnosis of so called bijective connection (BC) graphs including hypercubes, twisted cubes, locally twisted cubes, crossed cubes, and Mobius cubes. Utilizing a helpful structure proposed by Hsu and Tan [20] that was called the extending star by Lin et al. [24], and noting the existence of a structured Hamiltonian path within any BC graph, we present a fast diagnostic algorithm to identify all faulty nodes in O(N) time, where N=2^n, n>=4, stands for the total number of nodes in the n-dimensional BC graph. As a result, this algorithm is significantly superior to Dahura-Massons algorithm when applied to BC graphs.

A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n?6 and 1≤m≤?n/2?-1, a family of 2m disjoint k-dimensional tori of size 2 s 1 × 2 s 2 × ? × 2 s k each can be embedded in an n-dimensional crossed cube with unit dilation, where each si?2, ? i = 1 k s i = n - m , and max1≤i≤k{si}?3 if n is odd and m = n - 3 2 ; otherwise, max1≤i≤k{si}?n-2m-1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.

Hamiltonian Cycle Embedding in Hierarchical Crossed Cubes

The hypercube has been widely used as the interconnection network in parallel computers. The crossed cube is a variation of hypercube and preserves many of its desirable properties. The hierarchical crossed cube draws upon constructions used within the hypercube and also the crossed cube. The hierarchical crossed cube is suitable for massively parallel systems with thousands of processors and owns many alluring features, such as symmetry and logarithmic diameter. In this paper, we adopt the concept of Hamiltonian cycles pattern to provide a constructive algorithm to generate a Hamiltonian cycle of the hierarchical crossed cube.

The Existence of Two Mutually Independent Hamiltonian Cycles in Hypercube-Like Graphs

The problem of whether or not there are mutually independent hamiltonian cycles in interconnection networks has attracted a great attention in recent years. In this paper, we will show that most of

Embed Geodesic Cycles into Möbius Cubes

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Efficient Algorithms for Embedding Cycles in Augmented Cubes

-dimensional hypercube-like graphs have two mutually independent hamiltonian cycles. Moreover, we also develop a systematic linear time algorithm for constructing two mutually independent hamiltonian cycles in the

The two-equal-disjoint path cover problem of Matching Composition Network

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Geodesic pancyclicity and balanced pancyclicity of Augmented cubes

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Embedding geodesic and balanced cycles into hypercubes

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