With the rapid developments in the Internet of Things (IoT), low power wide area networks (LPWAN) framework, which is a low-power, long-distance communication method, is attracting attention. However, in LPWAN, the access time is limited by Duty Cycle (DC) to avoid mutual interference. Packet-level index modulation (PLIM) is a modulation scheme that uses a combination of the transmission time and frequency channel of a packet as an index, enabling throughput expansion even under DC constraints. The indexes used in PLIM are transmitted according to the mapping. However, when many sensors access the same index, packet collisions occur owing to selecting the same index. Therefore, we propose a mapping design for PLIM using mathematical optimization. The mapping was designed and modeled as a quadratic integer programming problem. The results of the computer simulation evaluations were used to realize the design of PLIM, which achieved excellent sensor information aggregation in terms of environmental monitoring accuracy.

The bin packing problem is a problem of finding an assignment of a sequence of items to a minimum number of bins, each of capacity one. An online algorithm for the bin packing problem is an algorithm that irrevocably assigns each item one by one from the head of the sequence. Gutin, Jensen, and Yeo (2006) considered a version in which all items are only of two different sizes and the online algorithm knows the two possible sizes in advance, and gave an optimal online algorithm for the case when the larger size exceeds 1/2. In this paper we provide an optimal online algorithm for some of the cases when the larger size is at most 1/2, on the basis of a framework that facilitates the design and analysis of algorithms.

The construction of a Huffman code can be understood as the problem of finding a full binary tree such that each leaf is associated with a linear function of the depth of the leaf and the sum of the function values is minimized. Fujiwara and Jacobs extended this to a general function and proved the extended problem to be NP-hard. The authors also showed the case where the functions associated with leaves are each non-decreasing and convex is solvable in polynomial time. However, the complexity of the case of non-decreasing non-convex functions remains unknown. In this paper we try to reveal the complexity by considering non-decreasing non-convex functions each of which takes the smaller value of either a linear function or a constant. As a result, we provide a polynomial-time algorithm for two subclasses of such functions.

Information exchange through a relay node is attracting attention for applying machine-to-machine communications. If the node demodulates the received signal in relay processing confidentially, the information leakage through the relay station is a problem. In wireless MIMO switching, the frequency spectrum usage efficiency can be improved owing to the completion of information exchange within a short time. This study proposes a novel wireless MIMO switching method for secure information exchange. An overloaded situation, in which the access nodes are one larger than the number of antennas in the relay node, makes the demodulation of the relay node difficult. The access schedule of nodes is required for maintaining the overload situation and the high information exchange efficiency. This study derives the equation model of the access schedule and constructs an access schedule with fewer time periods in the integer programming problem. From the computer simulation, we confirm that the secure capacity of the proposed MIMO switching is larger than that of the original one, and the constructed access schedule is as large as the ideal and minimum time period for information exchange completion.

In the bin packing problem, we are asked to place given items, each being of size between zero and one, into bins of capacity one. The goal is to minimize the number of bins that contain at least one item. An online algorithm for the bin packing problem decides where to place each item one by one when it arrives. The asymptotic approximation ratio of the bin packing problem is defined as the performance of an optimal online algorithm for the problem. That value indicates the intrinsic hardness of the bin packing problem. In this paper we study the bin packing problem in which every item is of either size α or size β (≤ α). While the asymptotic approximation ratio for $alpha > rac{1}{2}$ was already identified, that for $alpha leq rac{1}{2}$ is only partially known. This paper is the first to give a lower bound on the asymptotic approximation ratio for any $alpha leq rac{1}{2}$, by formulating linear optimization problems. Furthermore, we derive another lower bound in a closed form by constructing dual feasible solutions.

The performance of online algorithms for the bin packing problem is usually measured by the asymptotic approximation ratio. However, even if an online algorithm is explicitly described, it is in general difficult to obtain the exact value of the asymptotic approximation ratio. In this paper we show a theorem that gives the exact value of the asymptotic approximation ratio in a closed form when the item sizes and the online algorithm satisfy some conditions. Moreover, we demonstrate that our theorem serves as a powerful tool for the design of online algorithms combined with mathematical optimization.

This paper presents an algorithm to arrange a large number of antenna elements in the limited space of massive MIMO base station antenna without degrading the communication quality under a street-cell line-of-sight environment in mobile communications. The proposed algorithm works by using mathematical optimization in which the objective function is the correlation coefficient between the channel responses of two elements of the base station antenna, according to an algorithm constructed based on the results obtained through basic examinations of the characteristics of the correlation coefficient between channel responses. The channel responses are computed by using the propagation path information obtained by ray-tracing. The arrangements output by the proposed algorithm are mainly evaluated by channel capacity comparison with uniformly spaced arrangements on the vertical plane in single user and multiuser environments. The evaluation results of these arrangements in downlink demonstrate the superiority of the arrangements generated by the proposed algorithm, especially in term of robustness against an increase in the number of users.