Browsing by Author "Kung, Tzu-Liang"

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An Algorithmic Approach to Conditional-Fault Local Diagnosis of Regular Multiprocessor Interconnected Systems under the PMC Model
(2013-03-01)
Lin, Cheng-Kuan
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Kung, Tzu-Liang
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Tan, Jimmy J. M.
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資訊工程學系
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Department of Computer Science
System-level diagnosis is a crucial subject for maintaining the reliability of multiprocessor interconnected systems. Consider a system composed of N independent processors, each of which tests a subset of the others. Under the PMC diagnosis model, Dahbura and Masson [10] proposed an O(N-2,N-5) algorithm to identify the set of faulty processors in a t-diagnosable system, in which at most t processors are permanently faulty. In this paper, we establish some sufficient conditions so that a t-regular system can be conditionally (2t - 1)-diagnosable, provided every fault-free processor has at least one fault-free neighbor. Because any t-regular system is no more than t-diagnosable, the approached diagnostic capability is nearly double the classical one-step diagnosability. Furthermore, a correct and complete method is given which exploits these conditions and the presented branch-of-tree architecture to determine the fault status of any single processor. The proposed method has time complexity O(t(2)), and thus can diagnose the whole system in time O(t(2)N). In short, not only could the diagnostic capability be proved theoretically, but also it is feasible from an algorithmic perspective.
Conditional-Fault Diagnosability of Multiprocessor Systems with an Efficient Local Diagnosis Algorithm under the PMC Model
(2011-10-01)
Lin, Cheng-Kuan
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Kung, Tzu-Liang
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Tan, Jimmy J. M.
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資訊工程學系
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Department of Computer Science
Diagnosis is an essential subject for the reliability of multiprocessor systems. Under the PMC diagnosis model, Dahbura and Masson [12] proposed a polynomial-time algorithm with time complexity O(N(2.5)) to identify all the faulty processors in a system with N processors. In this paper, we present a novel method to diagnose a conditionally faulty system by applying the concept behind the local diagnosis, introduced by Somani and Agarwal [30], and formalized by Hsu and Tan [18]. The goal of local diagnosis is to identify the fault status of any single processor correctly. Under the PMC diagnosis model, we give a sufficient condition to estimate the local diagnosability of a given processor. Furthermore, we propose a helpful structure, called the augmenting star, to efficiently determine the fault status of each processor. For an N-processor system in which every processor has an O(log N) degree, the time complexity of our algorithm to diagnose any given processor is O((log N)(2)), provided that each processor can construct an augmenting star structure of full order in time O((log N)(2)) and the time for a processor to test another one is constant. Therefore, the time totals to O(N(log N)(2)) for diagnosing the whole system.
Disjoint cycles in hypercubes with prescribed vertices in each cycle
(2013-12-01)
Lin, Cheng-Kuan
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Tan, Jimmy J. M.
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Hsu, Lih-Hsing
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Kung, Tzu-Liang
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資訊工程學系
A graph G is spanning r-cyclable of order t if for any r nonempty mutually disjoint vertex subsets A(1), A(2) ,..., A(r) of G with vertical bar A(1) boolean OR A(2) boolean OR ... boolean OR A(r)vertical bar <= t, there exist r disjoint cycles C-1, C-2,...,Cr of G such that C-1 boolean OR C-2 boolean OR ... C-r spans G, and C-t contains A(i) for every i. In this paper, we prove that the n-dimensional hypercube Q(n) is spanning 2-cyclable of order n - 1 for n >= 3. Moreover, Q(n) is spanning k-cyclable of order k if k <= n - 1 for n >= 2. The spanning r-cyclability of a graph G is the maximum integer t such that G is spanning r-cyclable of order k for k = r, r + 1,..., t but is not spanning r-cyclable of order t + 1. We also show that the spanning 2-cyclability of Q(n) is n - for n >= 3. (C) 2013 Elsevier B.V. All rights reserved.
Fault-free mutually independent Hamiltonian cycles of faulty star graphs
(2011)
Kung, Tzu-Liang
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Lin, Cheng-Kuan
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Liang, Tyne
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Tan, Jimmy J. M.
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Hsu, Lih-Hsing
The star graph interconnection network has been recognized as an attractive alternative to the hypercube for its nice topological properties. Unlike previous research concerning the issue of embedding exactly one Hamiltonian cycle into an injured star network, this paper addresses the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty star network. To be precise, let SG(n) denote an n-dimensional star network in which f <= n - 3 edges may fail accidentally. We show that there exist (n - 2 - f)-mutually independent Hamiltonian cycles rooted at any vertex in SGn if n epsilon {3, 4}, and there exist (n - 1 - f)-mutually independent Hamiltonian cycles rooted at any vertex in SG(n) if n >= 5.
On the bipanpositionable bipanconnectedness of hypercubes
(2009-03-01)
Kung, Tzu-Liang
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Lin, Cheng-Kuan
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Liang, Tyne
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Hsu, Lih-Hsing
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Tan, Jimmy J. M.
A bipartite graph G is bipanconnected if, for any two distinct vertices x and y of G, it contains an vertical bar x,y vertical bar-path of length l for each integer l satisfying d(G)(x, y) <= l <= vertical bar V(G)vertical bar - 1 and 2 vertical bar(l - d(G)(x, y)), where d(G)(x, y) denotes the distance between vertices x and y in G and V(G) denotes the vertex set of G. We say a bipartite graph G is bipanpositionably bipanconnected if, for any two distinct vertices x and y of G and for any vertex z is an element of V(G) - (x, y), it contains a path P(l,k) of length l Such that x is the beginning vertex of P(l,k), z is the (k + 1)-th vertex of P(l,k), and y is the ending vertex of P(l,k) for each integer l satisfying d(G)(x, z) + d(G)(y, z) <= l <= vertical bar V(G)vertical bar - 1 and 2 vertical bar(l - d(G)(x, z) - d(G)(y, z)) and for each integer k satisfying d(G)(x, z) <= k <= l -d(G)(y, z) and 2 vertical bar(k - d(G)(x, z)). In this paper, we prove that an n-cube is bipanpositionably bipanconnected if n >= 4. As a consequence, many properties of hypercubes, such as bipancyclicity, bipanconnectedness, bipanpositionable Hamiltonicity, etc., follow directly from our result. (C) 2008 Elsevier B.V. All rights reserved.
On the Enhanced Hyper-hamiltonian Laceability of Hypercubes
(2009)
Tsai, Tsung-Han
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Kung, Tzu-Liang
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Tan, Jimmy J. M.
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Hsu, Lih-Hsing
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資訊工程學系
A bipartite graph is hamiltonian laceable if there exists a hamiltonian path between any two vertices that are in different partite sets. A hamiltonian laceable graph G is said to be hyper-hamiltonian laceable if, for any vertex v of G, there exists a hamiltonian path of G - {v} joining any two vertices that are located in the same partite set different from that of v. In this paper, we further improve the hyper-hamiltonian laceability of hypercubes by showing that, for any two vertices x, y from one partite set of Q(n), n >= 4, and any vertex w from the other partite set, there exists a hamiltonian path H of Q(n) - {w} joining x to y such that d(H)(X, Z) = l for any vertex z is an element of V(Q(n)) - {x, y, w} and for every integer l satisfying both d(Qn) (x, z) <= l <= 2(n) - 2 - d(Qn) (z, y) and 2 vertical bar(l - d(Qn) (x, z)). As a consequence, many attractive properties of hypercubes follow directly from our result.
On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube
(2014-02-01)
Kung, Tzu-Liang
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Lin, Cheng-Kuan
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Hsu, Lih-Hsing
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資訊工程學系
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Department of Computer Science
Hsieh and Yu (2007) first claimed that an injured n-dimensional hypercube Q (n) contains (n-1-f)-mutually independent fault-free Hamiltonian cycles, where fa parts per thousand currency signn-2 denotes the total number of permanent edge-faults in Q (n) for na parts per thousand yen4, and edge-faults can occur everywhere at random. Later, Kueng et al. (2009a) presented a formal proof to validate Hsieh and Yu's argument. This paper aims to improve this mentioned result by showing that up to (n-f)-mutually independent fault-free Hamiltonian cycles can be embedded under the same condition. Let F denote the set of f faulty edges. If all faulty edges happen to be incident with an identical vertex s, i.e., the minimum degree of the survival graph Q (n) -F is equal to n-f, then Q (n) -F contains at most (n-f)-mutually independent Hamiltonian cycles starting from s. From such a point of view, the presented result is optimal. Thus, not only does our improvement increase the number of mutually independent fault-free Hamiltonian cycles by one, but also the optimality can be achieved.