Garng M. Huang

A fast distributed shortest path algorithm for a class of hierarchically clustered data networks

A distributed algorithm is presented that can be used to solve the single-destination shortest path (SDSP) problem or the all-pairs shortest path (APSP) problem for a class of clustered data networks. The network graph is assumed to be characterized with a balanced hierarchically clustered (BHC) topology. The BHC topology is introduced in this paper and is shown to be a realistic characterization for a large class of interconnected data networks. For certain types of BHC topologies, the SDSP problem can be solved with computation and communication time complexities of O(log n), assuming one processor is available at each of the n number of nodes. Assuming p processors are available at each node, computation and communication time complexities of O((n/p) log n) and O(n log n) are achievable, respectively, for solving the APSP problem. It is also shown that the algorithm converges in an asynchronous environment. >

Complexity of gradient projection method for optimal routing in data networks

In this paper, we derive a time-complexity bound for the gradient projection method for optimal routing in data networks. This result shows that the gradient projection algorithm of Goldstein-Levitin-Poljak type formulated by Bertsekas (1982), Bertsekas and Gallager (1987) and Bertsekas et al. (1984) converges to within /spl epsi/ in relative accuracy in O(/spl epsi//sup -2/h/sub min/N/sub max/) number of iterations, where N/sub max/ is the number of paths sharing the maximally shared link, and h/sub min/ is the diameter of the network. Based on this complexity result, we also show that the one-source-at-a-time update policy has a complexity bound which is O(n) times smaller than that of the all-at-a-time update policy, where n is the number of nodes in the network. The result of this paper argues for constructing networks with low diameter for the purpose of reducing complexity of the network control algorithms. The result also implies that parallelizing the optimal routing algorithm over the network nodes is beneficial.

A fast distributed shortest path algorithm for a class of hierarchically structured data networks

A distributed algorithm is presented which finds the shortest path from every node in the network to a given destination node. The network topology is assumed to be organizable into a generalized balanced-tree hierarchy (BH). The BH topology is introduced and characterized, and it is shown that most large interconnected data networks are of this type. It is also shown that the algorithm converges in an asynchronous environment. Therefore, some of the difficulties associated with synchronizing the order of events can be avoided in the actual implementation of the proposed algorithm.<<ETX>>

A highly parallel algorithm for multistage optimization problems and shortest path problems

Abstract It appears that all of the known algorithms for solving multistage optimization problems are based explicitly on standard dynamic programming concepts. Such algorithms are inherently serial in the sense that computation must be completed at the current stage before meaningful computation can begin at the next stage. In this paper we present a technique which recursively divides the original problem into a set of smaller problems which can be solved in parallel. This technique is based on the recursive application of a simple aggregation procedure. For a multistage process with n stages, we show that our new algorithm can achieve a time complexity of O(log n). In contrast, competing algorithms based exclusively on the standard dynamic programming technique can only achieve a time complexity of Φ(n). The new algorithm is designed to operate on a tightly coupled parallel computer. As some important applications, it is shown that our algorithm can serve as a fast and efficient means of decoding convolutional codes, solving shortest path problems, and determining minimum-fuel flight paths.

A Parallel Textured Algorithm for Optimal Power Flow Analysis

A parallel textured algorithm is developed to solve the optimal real power flow problem which is reformulated in terms of line flows. In the textured method, the large-scale system is divided into small subsystems which are organized systematically on several levels. Each level consists of several mutually independent subsystems so that if the external flows in a level are fixed, the subsystem subproblems at the same level can be solved independently and concurrently. Consequently, the final optimal solution of the whole system can be obtained by combining these subsystem solutions. This paper relaxed the locality property required in our earlier work on reactive power control, but some extra requirements on the overlapping networks are needed to insure the convergence to the true solution. The extension enables us to deal with real power generation dispatch control, in which the locality property usually does not apply.

Impact analysis of wind generation on voltage stability and system load margin

Due to the environmental concerns and induced political incentives, wind power penetration has been increasing in many countries around the world. However, wind power generation is very different from conventional power generation due to stochastic and intermittent nature of the wind. The wind power may not be available or generating the demanded amount as needed. Thus, these mandates to promote wind power need to be balanced by studies on their impacts on power system operations and control. However, new approach is needed to properly quantify the voltage stability of power system. Accordingly, this paper addresses the modeling of the stochastic and intermittent wind generation and its use to predict the associated stability margin in terms of system load margin. To model the variation nature of stochastic and intermittent wind power injection as the load increases, we propose to use the Weibull distribution of wind speed to model the intermittent factor. The slip of asynchronous wind generators is introduced as a new state variable, and thus new power balance equations including the slip as a state variable are formulated. The balance between the average electromechanical power conversion and mechanical power of wind turbines is utilized to incorporate wind stochastic and intermittent uncertainty. As a first step, we investigate the impacts of the wind generation on static power flows. In terms nonlinear control terminology, we are investigating the stochastic nature of the equilibrium points associated with the uncertainty of the wind generation. Accordingly, we derive a novel sensitivity index of voltage stability considering the stochastic and intermittent nature of wind speed through the slip effect, using the Jacobian matrix for the newly formulated power flow equations. In addition, the probabilistic stability margins in terms of load for various wind speed distribution and penetration are investigated by use of the proposed CPF and Monte Carlo method. The proposed methods are illustrated on the IEEE 39-bus system and the results show that the stochastic and intermittent wind power injection will significantly affect the stability margin and its slip.

An efficient load-balancing processor scheduling algorithm for parallelization of Gauss-Seidel type algorithms

Abstract The paper extends our earlier results on the parallelization of Gauss-Seidel (G-S) algorithms for power flow analysis. In the earlier paper, we formulate the parallelizing process as a basic coloring problem, which satisfies the constraint that no directly connected vertices have the same color, without worrying about the constraint on the number of available processors. In this paper, this extra constraint is considered. A heuristic approach is developed to maximize the processor efficiency under the number of processor constraint. The idea is to fully utilize the processor resource, to balance the computational load, and to maximize the use of newly computed data for faster convergence. Some examples and test results are described in this paper.

Fast Parallel Hierarchical Aggregation/Disaggregation Algorithms for Multistage Optimization Problems and Shortest Path Problems

It appears that all of the known algorithms for solving multistage optimization problems are based explicitly on standard dynamic programming concepts. Such algorithms are inherently serial in the sense that computation must be completed at the current stage before meaningful computation can begin at the next stage. In this paper we present a technique which recursively divides the original problem into a set of smaller problems which can be solved in parallel. This technique is based on a hierarchical (recursive) structure of aggregation and disaggregation. For a multistage process with n stages, we show that our new algorithm achieves a time complexity of O(log n), assuming O(1) states per stage. However, algorithms based only on the standard dynamic programming technique can achieve a time complexity no better than O(n). Our new algorithm is designed to operate on tightly coupled parallel computer. As some important applications, it is shown that our algorithm can serve as a fast and efficient means of decoding convolutional codes, solving routing problems in data networks, and determining minimum-fuel flight paths.

A new HAD algorithm for optimal routing of hierarchically structured data networks

In this paper a new algorithm based on aggregation/disaggregation and decomposition/composition (HAD) scheme is proposed to solve the optimal routing problems (ORP) for hierarchically structured networks. Our algorithm has two major differences with the existing HAD algorithms for hierarchically clustered networks: 1. Our algorithm works with networks which are more general than networks with clustered structure; 2. Our algorithm parallelizes the computations for different commodities so that it speeds up with a parallel time complexity of O(mlog/sup 2/(n)), which is much less than O(Mlog/sup 2/(n)) needed for the existing HAD algorithms, for an n-node network with M commodities. Here, m is a positive number usually much smaller than M and is a function of the patterns of all the commodities. The implementation of the algorithm for a 200-node network is simulated using the OPNET simulation package.