Use Quickest Path to Evaluate the Performance for An E-Commerce Network

In the E-Commerce network, it is an important issue to reduce the transmission time. The quickest path problem is to find the path in the network to send a given amount of data from the source to the sink with minimum transmission time. This problem traditionally assumed that the capacity of each arc in the network is deterministic. However, the capacity of each arc is stochastic due to failure, maintenance, etc. in many real-life networks. This paper proposes a simple algorithm to evaluate the probability that d units of data can be sent through the E-Commerce network within T units of time. Such a probability is a performance index for E-Commerce networks

Quality Management for an E-Commerce Network under Budget Constraint

In general, several types of information data are transmitted through an E-Commerce network simultaneously. Each type of information data is set to one type of commodity. Under the budget constraint, this paper studies the probability that a given amount of multicommodity can be transmitted through an E-Commerce network, where each node and each arc has several possible capacities. We may take this probability as a performance index for this network. Based on the properties of minimal paths, a simple algorithm is proposed to generate all lower boundary points for (d1 ,d2 ,…,dp ;C) where di is the demand of commodity i and C is the budget. The probability can then be calculated in terms of such points

Building Reliable Budget-Based Binary-State Networks

Everyday life is driven by various network, such as supply chains for distributing raw materials, semi-finished product goods, and final products; Internet of Things (IoT) for connecting and exchanging data; utility networks for transmitting fuel, power, water, electricity, and 4G/5G; and social networks for sharing information and connections. The binary-state network is a basic network, where the state of each component is either success or failure, i.e., the binary-state. Network reliability plays an important role in evaluating the performance of network planning, design, and management. Because more networks are being set up in the real world currently, there is a need for their reliability. It is necessary to build a reliable network within a limited budget. However, existing studies are focused on the budget limit for each minimal path (MP) in networks without considering the total budget of the entire network. We propose a novel concept to consider how to build a more reliable binary-state network under the budget limit. In addition, we propose an algorithm based on the binary-addition-tree algorithm (BAT) and stepwise vectors to solve the problem efficiently

Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance

We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional numerical freedom, combined with the loop-free topology of the tree network, allows one to maximally exploit the internal gauge invariance of tensor networks, ultimately leading to a computationally flexible and efficient algorithm able to treat open and periodic boundary conditions on the same footing. We benchmark the novel approach against the 1D Ising model in transverse field with periodic boundary conditions and discuss the strategy to cope with the broken translational invariance generated by the network structure. We then perform investigations on a state-of-the-art problem, namely the bilinear-biquadratic model in the transition between dimer and ferromagnetic phases. Our results clearly display an exponentially diverging correlation length and thus support the most recent guesses on the peculiarity of the transition.Comment: 11 pages, 13 figure

Perron vector optimization applied to search engines

In the last years, Google's PageRank optimization problems have been extensively studied. In that case, the ranking is given by the invariant measure of a stochastic matrix. In this paper, we consider the more general situation in which the ranking is determined by the Perron eigenvector of a nonnegative, but not necessarily stochastic, matrix, in order to cover Kleinberg's HITS algorithm. We also give some results for Tomlin's HOTS algorithm. The problem consists then in finding an optimal outlink strategy subject to design constraints and for a given search engine. We study the relaxed versions of these problems, which means that we should accept weighted hyperlinks. We provide an efficient algorithm for the computation of the matrix of partial derivatives of the criterion, that uses the low rank property of this matrix. We give a scalable algorithm that couples gradient and power iterations and gives a local minimum of the Perron vector optimization problem. We prove convergence by considering it as an approximate gradient method. We then show that optimal linkage stategies of HITS and HOTS optimization problems verify a threshold property. We report numerical results on fragments of the real web graph for these search engine optimization problems.Comment: 28 pages, 5 figure

Multi-Objective Model to Improve Network Reliability Level under Limited Budget by Considering Selection of Facilities and Total Service Distance in Rescue Operations

Sudden disasters may damage facilities, transportation networks and other critical infrastructures, delay rescue and bring huge losses. Facility selection and reliable transportation network play an important role in emergency rescue. In this paper, the reliability level between two points in a network is defined from the point of view of minimal edge cut and path, respectively, and the equivalence of these two definitions is proven. Based on this, a multi-objective optimization model is proposed. The first goal of the model is to minimize the total service distance, and the second goal is to maximize the network reliability level. The original model is transformed into a model with three objectives, and the three objectives are combined into one objective by the method of weighting. The model is applied to a case, and the results are analyzed to verify the effectiveness of the model