A reduced diameter interconnection network

A parallel algorithm for constructing independent spanning trees in twisted cubes

Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the n-dimensional twisted cube is edge-pancyclic for n ≥ 3. That is, for any (x,y) ∈ E(TQ n ) (n ≥ 3) and any integer l with 4 ≤ l ≤ 2 n , a cycle C of length l can be embedded with dilation 1 into TQ n such that (x,y) is in C. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore, TQ n is also a node-pancyclic graph for n ≥ 3.

Constructing edge-disjoint spanning trees in twisted cubes

This paper proposes a set of techniques to restore the regularity of a Boolean n-cube network in the presence of node failures, and algorithms to effectively route messages among the surviving nodes. An analytical model to evaluate the degradation of a damaged network is also presented. One way to restore the regularity of a damaged Boolean n-cube network is by simply disabling the nodes with more than one bad neighbor. The remaining network is called a '1-degraded subnet'. A very simple optimal-path routing algorithm, which requires each node to know only its neighbor's status, is developed for such a subnet. Since many nonfaulty nodes may have to be disabled in constructing a 1-degraded subnet, the authors further develop a heuristic algorithm to restore the network's regularity by constructing a 'subnet connected with optimal paths (SCOP)', where only a few nodes must be disabled. The routing algorithm used in 1-degraded subnets also works for SCOPs. To preserve the processing power of the network, they also propose a two-level hierarchical fault-tolerant routing scheme without disabling any nodes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The dimensions of twisted cubes are only limited to odd integers. In this paper, we first extend the dimensions of twisted cubes to all positive integers. Then, we introduce the concept of the restricted faulty set into twisted cubes. We further prove that under the condition that each node of the n-dimensional twisted cube TQ n has at least one fault-free neighbor, its restricted connectivity is 2n ? 2, which is almost twice as that of TQ n under the condition of arbitrary faulty nodes, the same as that of the n-dimensional hypercube. Moreover, we provide an O(NlogN) fault-free unicast algorithm and simulations result of the expected length of the fault-free path obtained by our algorithm, where N denotes the node number of TQ n . Finally, we propose a polynomial algorithm to check whether the faulty node set satisfies the condition that each node of the n-dimensional twisted cube TQ n has at least one fault-free neighbor.

Optimal fault-tolerant embedding of paths in twisted cubes

Server-centric data center architecture has been proposed to provide high throughput, scalable construction and error tolerance with commodity servers and switches for cloud data centers. To fully utilize those advantages of server-centric data center, an effective routing algorithm to find high quality multiple paths in Server-centric network is needed. However, current routing algorithms cannot achieve this completely: (1) the state-of-art routing algorithms in server-centric data center just consider hop count when selecting paths; (2) traditional multi-constraint QoS routing algorithms only find one feasible path and are usually switch-oriented; (3) present multi-path algorithms cannot guarantee the performance of the founded paths. In this paper, we propose a multi-constrained routing algorithm for server-centric data centers, named Server-Centric Multi-Constrained Routing Algorithm (SCRAT). This algorithm exploits the topology features of the Server-Centric data center to decrease the algorithm complexity and returns optimal and feasible paths simultaneously. In simulations, SCRAT has a very high probability (more than 96 %) to find the exact optimal path, and the cost of the optimal path found in SCRAT is about 10 % less compared with path found in previous TS_MCOP. Compared with previous MPTCP, SCRAT reduces the path delay by 18 % less and increase the bandwidth by 20 %.KeywordsTraditional Data Center NetworksServer-centric NetworkFeasible PathOriginal Routing AlgorithmOptimal PathThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we consider the routing and wavelength assignment problem in a wavelength routed all optical network. Inspired by techniques from artificial intelligence, in particular the Blocking Island (BI) abstraction, we propose a simple and intelligent routing and wavelength assignment (RWA) algorithm: BI_RWA. This algorithm can be used in arbitrarily connected optical networks. In addition, it is general enough such that with some simple modifications, it can be applied to different optical networking scenarios: static or dynamic traffic, single or multiple fiber links between node pairs, with or without wavelength converters. We have conducted simulation experiments to evaluate the performance of our algorithm. The simulation is carried out in two parts: static traffic and dynamic traffic. The results will demonstrate that our RWA algorithm outperforms state-of-the-art related algorithms.

A graph G is pancyclic if, for every 4 ≤ l ≤ |V (G)|, G has a cycle of length l. A graph G is edge-pancyclic if, for an arbitrary edge e of G and every 4 ≤ l ≤ |V(G)|, G has a cycle of length l containing e. A graph G is node-pancyclic if, for an arbitrary node u of G and every 4 ≤ l ≤ |V (G)|, G has a cycle of length l containing u. The twisted cube is an important variant of the hypercube. Recently, Fan et al. proved that the n-dimensional twisted cube TQn is edge-pancyclic for every n ≥ 3. They also asked if TQn is edge-pancyclic with (n−3) faults for n ≥ 3. We find that TQn is not edge-pancyclic with only one faulty edge for any n ≥ 3. Then we prove that TQn is node-pancyclic with (\langle n/2\rangle − 1) faulty edges for every n ≥ 3. The result is optimal in the sense that with \langle n/2\rangle faulty edges, the faulty TQn is not node-pancyclic for any n ≥ 3.

We present a deterministic local routing algorithm that is guaranteed to find a path between any pair of vertices in a half-$\theta_6$-graph (the half-$\theta_6$-graph is equivalent to the Delaunay triangulation where the empty region is an equilateral triangle). The length of the path is at most $5/\sqrt{3} \approx 2.887$ times the Euclidean distance between the pair of vertices. Moreover, we show that no local routing algorithm can achieve a better routing ratio, thereby proving that our routing algorithm is optimal. This is somewhat surprising because the spanning ratio of the half-$\theta_6$-graph is 2, meaning that even though there always exists a path whose length is at most twice the Euclidean distance, we cannot always find such a path when routing locally. Since every triangulation can be embedded in the plane as a half-$\theta_6$-graph using $O(\log n)$ bits per vertex coordinate via Schnyder's embedding scheme [W. Schnyder, Embedding planar graphs on the grid, in Proceedings of the 1st Annual ACM--SIAM Symposium on Discrete Algorithms (SODA 1990), ACM, New York, SIAM, Philadelphia, 1990, pp. 138--148], our result provides a competitive local routing algorithm for every such embedded triangulation. Finally, we show how our routing algorithm can be adapted to provide a routing ratio of $15/\sqrt{3} \approx 8.660$ on two bounded degree subgraphs of the half-$\theta_6$-graph.

This paper presents an alternative simple loop-free bandwidth-efficient distributed routing algorithm for mobile ad hoc networks, denoted as distributed dynamic, routing (DDR). Although DDR benefits from classical concepts like zone and forest, unlike previous solutions it achieves several goals at the same time. Firstly, it provides different mechanisms to drastically reduce routing complexity and improve delay performance. Secondly, it is an infrastructureless in a strong sense: it does not even require a physical location information. Finally, zone naming is performed dynamically and broadcasting is reduced noticeably.

Sorting networks are an important application for parallel processing and also can be used as interconnection networks with fast and simple self routing algorithm. The odd-even transposition sorting networks are an important class of sorting networks because of the ease of hardware implementation. The paper investigates testing and fault tolerant properties of such networks for single stuck at crossing (stuck at X) and stuck at straight (stuck at T) faults in the comparators. We have proved that a single test vector is sufficient to detect all single and multiple stuck at T faults. For stuck at X faults, we have shown that the networks are 1-fault tolerant for large number of comparators. Analysis of several examples support the conjecture that these networks are 1-fault tolerant for all internal comparators.

Popularity of Mobile Wireless Sensor Network (MWSN) has increased tremendously due to the ability to connect the physical world with the virtual world. In MWSN, Sensor nodes move freely in a target area without the need of any special infrastructure. MWSN has attracted many researchers as it has introduced unique challenges in aspects like resource management, coverage, routing protocols, security in many applications such as target tracking in military applications, detection of catastrophic events, environment monitoring, health applications etc. Due to mobility, routing process in MWSN has become more complicated as connections in the network can change dynamically. This paper proposes a Mobility-Aware Multi-Objective Hybrid Routing Algorithm (MMOHRA) for Wireless Sensor Network (WSN). MMOHRA selects the best route and forwards the data packets from source to sink using multiple metrics such as Average Energy consumption, Control Overhead, Reaction Time, LQI, and HOP Count. Performance of MMOHRA is compared with Simple Hybrid Routing Protocol (SHRP) and Dynamic Multi-objective Routing Algorithm (DyMORA) using metrics such as Average Energy Consumption, Packet Delivery Ratio, and Jitter. MMOHRA improves the Average Energy Consumption (AEC) by a factor of 14.1% as compared with SHRP and 8.13 % as compared to DyMORA. MMOHRA outperformed SHRP and DyMORA in terms of packet Delivery Ratio (PDR) by 10.17 % and 9.83 % respectively.

The Mobius cubes are hypercube variants that give better performance with the same number of links and processors. We show that the diameter of the Mobius cubes is about 1/2 the diameter of the equivalent hypercube, and that the average number of steps between processors for a Mobius cube is about 2/3 of the average for a hypercube. We give an efficient routing algorithm for the Mobius cubes. This routing algorithm finds a shortest path and operates in time proportional to the dimension of the cube. We report results of simulation studies on the dynamic message-passing performance of the hypercube, the Twisted Cube of Hilbers et. al. [8], and the Mobius cubes. Our results agree with those of Abraham [2], showing that the Twisted Cube has worse dynamic performance than the hypercube. But our results show that the Mobius cubes and in particular the 1-Mobius cube have better dynamic performance than the hypercube.

Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary- or secondary-interference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100% throughput. However, previous work regarding Local Pooling focused mostly on obtaining abstract conditions and on networks with single-hop interference or single-hop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100% of this throughput. Regarding multihop traffic, we show that if the network satisfies only the single-hop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100% throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.