Yonghong Xiang - Academia.edu (original) (raw)

Papers by Yonghong Xiang

IEEE Transactions on Parallel and Distributed Systems, 2011

We prove that a k-ary 2-cube Q2k with three faulty edges but where every vertex is incident with ... more We prove that a k-ary 2-cube Q2k with three faulty edges but where every vertex is incident with at least two healthy edges is bipancyclic, if k ≥ 3, and k-pancyclic, if k ≥ 5 is odd (these results are optimal). We go on to show that when k ≥ 4 is even and n ≥ 3, any k-ary n-cube Qnk with at most 4n-5 faulty edges so that every vertex is incident with at least two healthy edges is bipancyclic, and that this result is optimal.

IEEE Transactions on Parallel and Distributed Systems, 2009

1. 'Bipanconnectivity and bipancyclicity in k-ary n-cubes.', IEEE transactions on parallel and... more 2009) 'Bipanconnectivity and bipancyclicity in k-ary n-cubes.', IEEE transactions on parallel and distributed systems., 20 (1). pp. 25-33.

Discrete Applied Mathematics, 2010

1. 'One-to-many node-disjoint paths in (n,k)-star graphs.', Discrete applied mathematics., 158... more 2010) 'One-to-many node-disjoint paths in (n,k)-star graphs.', Discrete applied mathematics., 158 (1). pp. 62-70.

We prove that a k-ary 2-cube Q k 2 with 3 faulty edges but where every vertex is incident with at... more We prove that a k-ary 2-cube Q k 2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k ≥ 3, and k-pancyclic, if k ≥ 5 is odd (these results are optimal).

In a multiprocessor network, sending a packet typically refers to start-up time and transmission ... more In a multiprocessor network, sending a packet typically refers to start-up time and transmission time. To optimize these two times, as opposed to earlier solutions, a spanning tree and multiple spanning trees are constructed to solve four types of broadcasting problems in an (n, k)-star graph: one-to-all or all-to-all broadcasting with either one-port or all-port communication model, respectively. Since the proposed spanning tree has an optimal height, both one-to-all and all-to-all broadcasting algorithms achieve nearly optimal start-up time and transmission time under all-port model and one-port model, and optimal transmission time under one-port model. By using multiple spanning trees, both one-to-all and all-to-all algorithms achieve nearly optimal transmission time under all-port model and one-port model.

IEEE Transactions on Parallel and Distributed Systems, 2008

The tree structure has received much interest as a versatile architecture for a large class of pa... more The tree structure has received much interest as a versatile architecture for a large class of parallel processing applications. Spanning trees in particular are essential tools for some important communication problems such as broadcasting and personalized communications. When it refers to communications, it always involves two costs. Specifically, sending a packet of b bytes along a link takes T s + bTc time, where Ts is the time to initialize (or start-up) the communication link and Tc is the latency to transmit a byte. To optimize these costs, a spanning tree is constructed to solve one-to-all broadcasting problem in an (n, k)-arrangement graph. Since the spanning tree has an optimal height, our algorithm achieves optimal start-up cost O(D(An,k))Ts and transmission cost O((m/k(n-k))Tc) under the all-port model, and optimal transmission cost O(mTc) under the one-port model

The augmented k-ary n-cube AQ n,k is a recently proposed interconnection network that incorporate... more The augmented k-ary n-cube AQ n,k is a recently proposed interconnection network that incorporates an extension of a k-ary n-cube Q k n inspired by the extension of a hypercube Qn to the augmented hypercube AQn (as developed by Choudom and Sunita). We extend a recent topological investigation of augmented k-ary n-cubes by proving that any augmented k-ary n-cube AQ n,k is edge-pancyclic and that AQ 2,k is panconnected.

Information Sciences, 2011

We define an interconnection network AQ n,k which we call the augmented kary n-cube by extending ... more We define an interconnection network AQ n,k which we call the augmented kary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQ n,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQ n,k : is a Cayley graph, and so is vertex-symmetric, but not edge-symmetric unless n = 2; has connectivity 4n−2 and wide-diameter at most max{(n−1)k−(n−2), k+7}; has diameter ⌊ k 3 ⌋+⌈ k−1 3 ⌉, when n = 2; and has diameter at most k 4 (n + 1), for n ≥ 3 and k even, and at most k 4 (n + 1) + n 4 , for n ≥ 3 and k odd.

In a k-ary n-cube Q k n with at most 2n − 2 faulty edges, let u and v be any two given nodes. Sup... more In a k-ary n-cube Q k n with at most 2n − 2 faulty edges, let u and v be any two given nodes. Suppose the number of healthy links of u is no more than that of v, and denote by m. In this paper, we find m disjoint paths between u and v.

IEEE Transactions on Parallel and Distributed Systems, 2011

We prove that a k-ary 2-cube Q2k with three faulty edges but where every vertex is incident with ... more We prove that a k-ary 2-cube Q2k with three faulty edges but where every vertex is incident with at least two healthy edges is bipancyclic, if k ≥ 3, and k-pancyclic, if k ≥ 5 is odd (these results are optimal). We go on to show that when k ≥ 4 is even and n ≥ 3, any k-ary n-cube Qnk with at most 4n-5 faulty edges so that every vertex is incident with at least two healthy edges is bipancyclic, and that this result is optimal.

IEEE Transactions on Parallel and Distributed Systems, 2009

1. 'Bipanconnectivity and bipancyclicity in k-ary n-cubes.', IEEE transactions on parallel and... more 2009) 'Bipanconnectivity and bipancyclicity in k-ary n-cubes.', IEEE transactions on parallel and distributed systems., 20 (1). pp. 25-33.

Discrete Applied Mathematics, 2010

1. 'One-to-many node-disjoint paths in (n,k)-star graphs.', Discrete applied mathematics., 158... more 2010) 'One-to-many node-disjoint paths in (n,k)-star graphs.', Discrete applied mathematics., 158 (1). pp. 62-70.

We prove that a k-ary 2-cube Q k 2 with 3 faulty edges but where every vertex is incident with at... more We prove that a k-ary 2-cube Q k 2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k ≥ 3, and k-pancyclic, if k ≥ 5 is odd (these results are optimal).

In a multiprocessor network, sending a packet typically refers to start-up time and transmission ... more In a multiprocessor network, sending a packet typically refers to start-up time and transmission time. To optimize these two times, as opposed to earlier solutions, a spanning tree and multiple spanning trees are constructed to solve four types of broadcasting problems in an (n, k)-star graph: one-to-all or all-to-all broadcasting with either one-port or all-port communication model, respectively. Since the proposed spanning tree has an optimal height, both one-to-all and all-to-all broadcasting algorithms achieve nearly optimal start-up time and transmission time under all-port model and one-port model, and optimal transmission time under one-port model. By using multiple spanning trees, both one-to-all and all-to-all algorithms achieve nearly optimal transmission time under all-port model and one-port model.

IEEE Transactions on Parallel and Distributed Systems, 2008

The tree structure has received much interest as a versatile architecture for a large class of pa... more The tree structure has received much interest as a versatile architecture for a large class of parallel processing applications. Spanning trees in particular are essential tools for some important communication problems such as broadcasting and personalized communications. When it refers to communications, it always involves two costs. Specifically, sending a packet of b bytes along a link takes T s + bTc time, where Ts is the time to initialize (or start-up) the communication link and Tc is the latency to transmit a byte. To optimize these costs, a spanning tree is constructed to solve one-to-all broadcasting problem in an (n, k)-arrangement graph. Since the spanning tree has an optimal height, our algorithm achieves optimal start-up cost O(D(An,k))Ts and transmission cost O((m/k(n-k))Tc) under the all-port model, and optimal transmission cost O(mTc) under the one-port model

The augmented k-ary n-cube AQ n,k is a recently proposed interconnection network that incorporate... more The augmented k-ary n-cube AQ n,k is a recently proposed interconnection network that incorporates an extension of a k-ary n-cube Q k n inspired by the extension of a hypercube Qn to the augmented hypercube AQn (as developed by Choudom and Sunita). We extend a recent topological investigation of augmented k-ary n-cubes by proving that any augmented k-ary n-cube AQ n,k is edge-pancyclic and that AQ 2,k is panconnected.

Information Sciences, 2011

We define an interconnection network AQ n,k which we call the augmented kary n-cube by extending ... more We define an interconnection network AQ n,k which we call the augmented kary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQ n,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQ n,k : is a Cayley graph, and so is vertex-symmetric, but not edge-symmetric unless n = 2; has connectivity 4n−2 and wide-diameter at most max{(n−1)k−(n−2), k+7}; has diameter ⌊ k 3 ⌋+⌈ k−1 3 ⌉, when n = 2; and has diameter at most k 4 (n + 1), for n ≥ 3 and k even, and at most k 4 (n + 1) + n 4 , for n ≥ 3 and k odd.

In a k-ary n-cube Q k n with at most 2n − 2 faulty edges, let u and v be any two given nodes. Sup... more In a k-ary n-cube Q k n with at most 2n − 2 faulty edges, let u and v be any two given nodes. Suppose the number of healthy links of u is no more than that of v, and denote by m. In this paper, we find m disjoint paths between u and v.