Yuan-Hsiang Teng

On mutually independent hamiltonian paths

Abstract Let P 1 = 〈 v 1 , v 2 , v 3 , … , v n 〉 and P 2 = 〈 u 1 , u 2 , u 3 , … , u n 〉 be two hamiltonian paths of G . We say that P 1 and P 2 are independent if u 1 = v 1 , u n = v n , and u i ≠ v i for 1 i n . We say a set of hamiltonian paths P 1 , P 2 , … , P s of G between two distinct vertices are mutually independent if any two distinct paths in the set are independent. We use n to denote the number of vertices and use e to denote the number of edges in graph G . Moreover, we use e to denote the number of edges in the complement of G . Suppose that G is a graph with e ≤ n − 4 and n ≥ 4 . We prove that there are at least n − 2 − e mutually independent hamiltonian paths between any pair of distinct vertices of G except n = 5 and e = 1 . Assume that G is a graph with the degree sum of any two non-adjacent vertices being at least n + 2 . Let u and v be any two distinct vertices of G . We prove that there are deg G ( u ) + deg G ( v ) − n mutually independent hamiltonian paths between u and v if ( u , v ) ∈ E ( G ) and there are deg G ( u ) + deg G ( v ) − n + 2 mutually independent hamiltonian paths between u and v if otherwise.

The globally Bi-3 * -connected property of the honeycomb rectangular torus

The honeycomb rectangular torus is an attractive alternative to existing networks such as mesh-connected networks in parallel and distributed applications because of its low network cost and well-structured connectivity. Assume that m and n are positive even integers with n>=4. It is known that every honeycomb rectangular torus HReT(m,n) is a 3-regular bipartite graph. We prove that in any HReT(m,n), there exist three internally-disjoint spanning paths joining x and y whenever x and y belong to different partite sets. Moreover, for any pair of vertices x and y in the same partite set, there exists a vertex z in the partite set not containing x and y, such that there exist three internally-disjoint spanning paths of G-{z} joining x and y. Furthermore, for any three vertices x, y, and z of the same partite set there exist three internally-disjoint spanning paths of G-{z} joining x and y if and only if n>=6 or m=2.

Local Diagnosis Algorithms for Multiprocessor Systems Under the Comparison Diagnosis Model

An efficient diagnosis is very important for a multiprocessor system. The ability to identify all the faulty devices in a multiprocessor system is known as diagnosability. In the comparison model, the diagnosis is performed by sending two identical signals from a processor to a pair of distinct neighbors, and then comparing their responses. Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity O(N5) to diagnose a system with a total number N of processors under the comparison model. Recently, some concepts, such as the conditional diagnosability and the local diagnosability, are concerned with the measure which is able to better reflect fault patterns in real systems. In this paper, we propose a specific structure, the balanced wind-bell-tree, and give an algorithm to determine the fault status of each processor for conditional local diagnosis under the comparison model. According to our results, a specific t-connected network with the balanced wind-bell-tree structure is conditionally (2t-1)°-diagnosable, and the time complexity to diagnose all the faulty processors is O(N(logN)2) with our algorithm, where N is the total number of the processors in the network.

The spanning laceability on the faulty bipartite hypercube-like networks

A w-container C(u,v) of a graph G is a set of w-disjoint paths joining u to v. A w-container of G is a w^*-container if it contains all the nodes of V(G). A bipartite graph G is w^*-laceable if there exists a w^*-container between any two nodes from different parts of G. Let n and k be any two positive integers with n>=2 and k=

A test round controllable local diagnosis algorithm under the PMC diagnosis model

Abstract An efficient diagnosis is very important for a multiprocessor system. The ability of identifying all the faulty devices in a multiprocessor system is known as diagnosability. The PMC model is the tested-based diagnosis with a processor performing the diagnosis by testing on the neighboring processors via the links between them. Recently, some researches such as the conditional diagnosability and the local diagnosability, are concerned with the measure which is able to better reflect fault patterns in real systems. In this paper, we propose a specific structure for local diagnosis. Under the PMC model, we design a test round controllable local diagnosis algorithm for a t ∗ -diagnosable network. For some conditional constraint, we give a conditional local diagnosis algorithm for a ( 2 t - 1 ) ∗ -diagnosable network. With our algorithm, a diagnosis is completed in k test rounds.

Honeycomb rectangular disks

In this paper, we propose a variation of honeycomb meshes. A honeycomb rectangular disk HReD(m, n) is obtained from the honeycomb rectangular mesh HReM(m, n) by adding a boundary cycle. A honeycomb rectangular disk HReD(m, n) is a 3-regular planar graph. It is obvious that the honeycomb rectangular mesh HReM(m, n) is a subgraph of HReD(m, n). We also prove that HReD(m, n) is hamiltonian. Moreover, HReD(m, n) - f remains hamiltonian for any f ∈ V (HReD(m, n)) ∪ E(HReD(m, n)) if n ≥ 6.

On the Channel Congestion of the Shortest-Path Routing for Unidirectional Hypercube Networks

Interconnection networks are emerging as an approach to solving system-level communication problems. An interconnection network is a programmable system that serves to transport data or messages between components/terminals in a network system. The hypercube is one of the most widely studied network structures for interconnecting a huge number of network components so that it is usually considered as the fundamental principle and method of network design. The unidirectional hypercube, which was proposed by Chou and Du (1990), is obtained by orienting the direction of each edge in the hypercube. Routing is crucial for almost all aspects of network functionalities. In this paper, we propose a dimension-ordered shortest-path routing scheme for unidirectional hypercubes and then analyze the incurred channel congestion from a worst-case point of view.

A Diagnosis Algorithm on the 2D-torus Network

In this article, we design a three test rounds diagnosis algorithm for a 2D-torus network. Suppose that TDT(n, m) is a 2D-torus network with \(n\ge 4\), \(m\ge 6\) and m being even. Let F be the faulty set in TDT(n, m). With our algorithm, a diagnosis on TDT(n, m) is completed in three test rounds if \(|F|\le 4\).

Combinatorial analysis of the subsystem reliability of the split-star network

Abstract The reliability of a generic system is the probability that the system is fully functional under a given suite of operational and environmental conditions over a given time period. In this paper, the subsystem reliability of the split-star network is derived using a combinatorial approach. Some numerical results of various simulation models are shown to validate the established analytical formulation.

On the Robust Approach to Data Inconsistency Detection of Sensor Networks

A sensor network is one popular candidate for the fundamental backbone of IoT (Internet of Things). Among the key technologies involved in sensor networks, fault detection techniques are indispensable for maintaining the availability of sensor applications. Chen et. al. (2006) presented a distributed fault detection (DFD) scheme to identify hard faults, such as power failures, crash faults, etc., in a sensor network, and later Jiang (2009) improved upon this scheme. In this paper, we develop a more robust fault detection scheme and apply it to locate data inconsistency between sensors, which is a frequent category of soft faults.