One of the features of a software-defined network (SDN) is a logically centralized control plane hosting one or more SDN controllers. As SDN controller placement can impact network performance, it is widely studied as the controller placement problem (CPP). For a cost-effective network design, network providers need to minimize the number of SDN controllers used in the network since each SDN controller incurs installation and maintenance costs. Moreover, the network providers need to deal with the failure of SDN controllers. Existing studies that consider SDN controller failures use the scheme of connecting each SDN switch to one Master controller and one or more Slave controllers. The problem with this scheme is that the computing capacity of each SDN controller cannot be used efficiently since one SDN controller handles the load of all SDN switches connected to it. The number of SDN controllers required can be reduced by distributing the load of each SDN switch among multiple SDN controllers. This paper proposes a controller placement model that allows the distribution against SDN controller failures. The proposed model determines the ratios of computing capacity demanded by each SDN switch on the SDN controllers connected to it. The proposed model also determines the number and placement of SDN controllers and the assignment of each SDN switch to SDN controllers. Controller placement is determined so that a network provider can continue to manage all SDN switches if no more than a certain number of SDN controller failures occur. We develop two load distribution methods: split and even-split. We formulate the proposed model with each method as integer linear programming problems. Numerical results show that the proposed model reduces the number of SDN controllers compared to a benchmark model; the maximum reduction ratio is 38.8% when the system latency requirement between an SDN switch and an SDN controller is 100[ms], the computing capacity of each SDN controller is 6 × 106[packets/s], and the maximum number of SDN controllers that can fail at the same time is one.

Ising machines have attracted attention, which is expected to obtain better solutions of various combinatorial optimization problems at high speed by mapping the problems to natural phenomena. A slot-placement problem is one of the combinatorial optimization problems, regarded as a quadratic assignment problem, which relates to the optimal logic-block placement in a digital circuit as well as optimal delivery planning. Here, we propose a mapping to the Ising model for solving a slot-placement problem with additional constraints, called a constrained slot-placement problem, where several item pairs must be placed within a given distance. Since the behavior of Ising machines is stochastic and we map the problem to the Ising model which uses the penalty method, the obtained solution does not always satisfy the slot-placement constraint, which is different from the conventional methods such as the conventional simulated annealing. To resolve the problem, we propose an interpretation method in which a feasible solution is generated by post-processing procedures. We measured the execution time of an Ising machine and compared the execution time of the simulated annealing in which solutions with almost the same accuracy are obtained. As a result, we found that the Ising machine is faster than the simulated annealing that we implemented.

The machine-to-machine (M2M) service network platform that accommodates and controls various types of Internet of Things devices has been presented. This paper investigates program file placement strategies for the M2M service network platform that achieve low blocking ratios of new task requests and accommodate as many tasks as possible in the dynamic scenario. We present four strategies for determining program file placement, which differ in the computation method and whether the relocation of program files being used by existing tasks is allowed or not. Simulation results show that a strategy based on solving a mixed-integer linear programming model achieves the lowest blocking ratio, but a heuristic algorithm-based strategy can be an attractive option by allowing recomputation of the placement when the placement cannot be obtained at the timing of new task request arrival.

Recently, Network Function Virtualization (NFV) has drawn attentions of many network researchers with great deal of flexibilities, and various network service chains can be used in an SDN/NFV environment. With the flexibility of virtual middlebox placement, how to place virtual middleboxes in order to optimize the performance of service chains becomes essential. Some past studies focused on placement problem of consolidated middleboxes which combine multiple functions into a virtual middlebox. However, when a virtual middlebox providing only a single function is considered, the placement problem becomes much more complex. In this paper, we propose a new heuristic method, the gradual switch clustering based virtual middlebox placement method, in order to improve the performance of service chains, with the constraints of end-to-end delay, bandwidth, and operation cost of deploying a virtual middlebox on a switch. The proposed method gradually finds candidate places for each type of virtual middlebox along with the sequential order of service chains, by clustering candidate switches which satisfy the constraints. Finally, among candidate places for each type of virtual middlebox, the best places are selected in order to minimize the end-to-end delays of service chains. The evaluation results, which are obtained through Mininet based extensive emulations, show that the proposed method outperforms than other methods, and specifically it achieves around 25% less end-to-end delay than other methods.

The Machine-to-Machine (M2M) service network platform accommodates M2M communications traffic efficiently by using tree-structured networks and the computation resources deployed on network nodes. In the M2M service network platform, program files required for controlling devices are placed on network nodes, which have different amounts of computation resources according to their position in the hierarchy. The program files must be dynamically repositioned in response to service quality requests from each device, such as computation power, link bandwidth, and latency. This paper proposes a Program File Placement (PFP) method for the M2M service network platform. First, the PFP problem is formulated in the Mixed-Integer Linear Programming (MILP) approach. We prove that the decision version of the PFP problem is NP-complete. Next, we present heuristic algorithms that attain sub-optimal but attractive solutions. Evaluations show that the heuristic algorithm based on the number of devices that share a program file reduces the total number of placed program files compared to the algorithm that moves program files based on their position.

In this paper, we propose a novel Autonomous Decentralized Control (ADC) scheme for indirectly controlling a system performance variable of large-scale and wide-area networks. In a large-scale and wide-area network, since it is impractical for any one node to gather full information of the entire network, network control must be realized by inter-node collaboration using information local to each node. Several critical network problems (e.g., resource allocation) are often formulated by a system performance variable that is an amount to quantify system state. We solve such problems by designing an autonomous node action that indirectly controls, via the Markov Chain Monte Carlo method, the probability distribution of a system performance variable by using only local information. Analyses based on statistical mechanics confirm the effectiveness of the proposed node action. Moreover, the proposal is used to implement traffic-aware virtual machine placement control with load balancing in a data center network. Simulations confirm that it can control the system performance variable and is robust against system fluctuations. A comparison against a centralized control scheme verifies the superiority of the proposal.

The label placement problem is one of the most important problems in geographic information systems, cartography, graph drawing, and graphical interface design. In this paper, we considered the label size maximization problem for points with axes-parallel rectangular labels that correspond to character strings and have different widths based on the number of characters. We propose an algorithm for computing the optimum size for the label size maximization problem in the 2-position model and a polynomial time algorithm for the problem in the 4-position model. Our algorithm cannot obtain the maximum value in the 4-position model because the label size maximization problem in the 4-position model is NP-hard. However, our algorithm is efficient in practice, as shown by computational experiments. Further, computational results for JR trains, subways and major private railroads in Tokyo are presented.

The label placement problem is one of the most important problems in geographic information systems, cartography, graph drawing and graphical interface design. In this paper, we consider the problem of labeling points and curves in maps drawn from digital data. In digital maps, a curve is represented as a set of points and consists of many small segments. The label for each curve must be placed alongside the corresponding curve. We define a continuous labeling space for points and curves, and present an algorithm using this space for positioning labels. Computational results for subway and JR train maps in Tokyo are presented.

Node placement optimization in ShuffleNets is a combinatorial optimization problem. In this paper, a new heuristic node placement algorithm, called Lookahead Algorithm, is proposed. Its performance is compared with the lower bounds derived in [1], as well as some existing algorithms in the literature. Significant reduction in weighted mean hop distance hd is obtained, especially when the traffic distribution in ShuffleNets is highly skewed. Consider a ShuffleNet with 8 nodes, the hd obtained using Lookahead Algorithm is only 1.90% above the lower bound under the skewed traffic distribution (with traffic skew factor γ = 100), and 16.04% under uniform random traffic distribution.