Graph-based output phase assignment for PLA minimization

The goore game (GG) is a model for collective decision making under uncertainty, which can be used as a tool for stochastic optimization of a discrete variable function. The GG has a fascinating property that can be resolved in a distributed manner with no intercommunication between the players. The game has found applications in many network applications, including sensor networks, quality-of-service routing, and social networks. In this paper, we introduce an extension of GG called cellular goore game (CGG) for the first time. The CGG is a network of GGs. In this network, each node (or subset of nodes in the network) plays the rule of referees, each of which participates in a GG with its neighboring players (voters) at any time. Like in GG, each player independently selects its optimal action between two available actions based on their gains and losses received from its adjacent referee. Players in CGG know nothing about how other players are playing or even how/why they are rewarded/penalized. The potential of the CGG is shown by providing an algorithm for finding a maximum clique in social networks. Our research provides the first-time study of the CGG for finding a maximum clique in graphs. The performance of the CGG-based algorithm for finding maximum clique is studied on the standard clique benchmark called DIMACS by several experiments. The obtained result shows that the CGG-based algorithm is superior to the existing algorithms in terms of finding maximum clique size and time.

The intent of maximum clique problem is to discover a clique of largest size or a complete subgraph in a graph; for a graph clique is a subgraph which is complete i.e., every vertex of that subgraph are adjacent to each other. It belongs to the category of the NP-hard problems, for which many solutions exist and many more are continuously being proposed. We are recapitulating the core idea and search strategies of few of the branch and bound based recently proposed algorithms. Intent of this work is to give a comparative study of newly proposed solutions to maximum clique problem which will be helpful to decide which algorithm is efficient for a given graph. It also instigates to design more efficient solutions for maximum clique problem.

Recently, the installation of the battery for the power system has been investigated. This study focuses on the optimal battery assignment method which assigns the batteries to contribute to the system stabilization against N-1 line accident. In this method, the optimal battery assignment and operation problem whose objective is the minimization of the phase difference fluctuation on all nodes caused by N-1 line accident at each branch is formulated. Then, the optimal battery assignment and the power supplies of batteries are determined by solving the formulated problem. However, this method requires a lot of computation time, because this method requires a large number of power flow calculations with high computational cost. This study proposes to apply the response surface method with the radial basis function networks to the optimal battery assignment and operation problem in order to reduce the number of the power flow calculations. This paper confirms the effectiveness of the proposed method through numerical experiments of the application to the IEEJ EAST 10-machine system model.

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.

The following problem is solved: determine a point on a tree having the property that the sum of the products of the intensities of its vertices by the corresponding distances to that point is a minimum. The proposed algorithm is reduced to the stepwise application to the tree of truncation of its vertices. A feasible interpretation of the problem is given.

In this paper, we first establish a Multi-Relation Granular Computing model by a given graph, and point out that all the reducts of the constructed Multi-Relation Granular Computing model are exactly all the minimal vertex covers of the corresponding graph. Thus, the vertex cover problem in graph theory can be converted to the knowledge reduction problem in rough set theory. Based on the conversion, we then introduce methods for dealing with the knowledge reduction problem to solve the vertex cover problem. In particular, we introduce a kind of method called the heuristic reduction algorithm based on entropy.

A genetic algorithm for optimal flow assignment in computer network

There will be a lot of NP- complete problems in graph theory and optimization process, as the most important problem in scientific engineering computing, now it is generally used genetic algorithm to solve. Therefore, this article will mainly study the basic theory of genetic algorithms and graph theory, and put forward the optimization algorithm in graph theory vertex cover problem in the specific application.

Graph matching is one of the most important problems in graph theory and combinatorial optimization, with many applications in various domains. Although meta-heuristic algorithms have had good performance on many NP-Hard and NP-Complete problems, but for graph matching problem, there were not reported superior solutions by these sort of algorithms. The reason of this inefficiency has not been investigated yet. In this paper it has been shown that Simulated Annealing (SA) as an instance of a meta-heuristic method is unlikely to be even close to the optimal solution for this problem. Mathematical and experimental results showed that the chance to reach to a partial solution, is very low, even for small number of true matches. In addition to theoretical discussion, the experimental results also verified our idea; for example, in two sample graphs with $10000$ vertices, the probability of reaching to a solution with at least three correct matches is about $0.02$ with simulated annealing.

This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the swarm assignment and trajectory optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.

Independent domination in finitely defined classes of graphs: Polynomial algorithms

We consider to identify an unknown Boolean function f by asking an oracle the functional values f(a) for a selected set of test vectors a ε {0,1}n. If f is known to be a positive function of n variables, the algorithm by Gainanov can achieve the goal by issuing O(mn) queries, where m = ¦minT(f)¦ + ¦maxF(f)¦ and minT(f) (resp. maxF(f)) denotes the set of minimal true vectors (resp. maximal false vectors) of f. However, it is not known whether this whole task including the generation of test vectors can be carried out in polynomial time in n and m or not. To partially answer this question, we propose here two algorithms that, given an unknown positive function f of n variables, decide whether f is 2-monotonic or not, and if f is 2-monotonic, output sets min T(f) and max F(f). The first algorithm uses O(nm 2+n 2 m) time and O(nm) queries while the second one uses O(n3m) time and O(n 3 m) queries.

Reversible parallel computation: An evolving space-model

We consider a finite buffer shared by multiple packet queues. Throughput can be considerably improved by partitioning the buffer space among the queues judiciously, especially under a high load regime. We formulate optimal buffer partitioning as a resource allocation problem, the solution of which is found through a greedy incremental algorithm in polynomial time. The rest of the work is devoted to applying the optimal buffer allocation strategy in different scenarios modeling a wireless downlink. First, the strategy is applied in a general parallel M/M/1/m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> system and a numerical study verifies that the strategy may boost the throughput considerably. Then, a multichannel extension of this system is considered when the users have different arrival rates and channels have different outage probabilities. Jointly optimal buffer space allocation and channel assignment problems in this scenario are shown to be separable. Lastly, buffer allocation is considered in a system where users need to be multiplexed and scheduled based on channel state. It is shown that this system can be modeled as a set of parallel M/G/1/m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> queues to which the optimum buffer allocation strategy is again applicable. The improvement brought by optimal buffer allocation to scheduling based solely on channel-state is explored. It is observed that buffer optimization can result in remarkable throughput increase on top of channel-based user selection.

Considers the optimal (i.e., minimum length) time slot assignment problem for variable bandwidth switching systems. Existing algorithms for this problem are known to be pseudo-polynomial. The practical question of finding a fast optimal algorithm, as well as the theoretical question of whether the above problem is NP-complete were left open. The authors present a technique to show polynomial time complexity of some time slot assignment algorithms. Such a technique applies to an algorithm proposed by Chalasani and Varma in 1991 (called the CV algorithm), as well as to a network flow based optimal algorithm, proposed in the present paper for the first time. The CV algorithm and the one proposed are slightly different. Thus, the authors give an answer to both the above questions, by establishing that the problem is in P, and by showing effective algorithms for it.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>