This paper reviews the historical aspect of contributions on the theory of analysis and diagnosis of linear circuits, which have been made by Japanese researchers in these twenty years. On papers of diagnosis, those related to element-value solvability (or determinability) are mainly reviewed. Some important problems are suggested.

Pilot-symbol-aided (PSA) channel estimation for OFDM wireless access systems enables the periodic estimation of channel frequency response by generating reference data from the received OFDM signals. The accuracy of this channel estimation can be improved through the average over a certain time period in each subcarrier-channel. However, the accuracy of the channel estimates by the average degrades as the Doppler shift is large due to a decrease in the average section size according to the Doppler shift for the tracking of the time-varying channel. This paper proposes a novel PSA channel estimation method to mitigate the influence of the noises and interferences. This method detects the channel estimates affected by the noises and interferences, and then removes them before the arithmetic or harmonic averaging to avoid propagating the influence of the noises and interferences. This paper also evaluated the proposed channel estimation method by clipping log-likelihood ratio (LLR) data to inspect the influence of the channel estimation on the LLR calculation by computer simulation.

An arborescence-net N is a directed connected communication network with arborescence structure. Some information to be distributed through N is supposed to have been written in a file and the written file is denoted by J, where the file means an abstract concept of information carrier. In this letter, we consider a problem of distributing copies of J through N from the root vertex to every vertex, where the cost of transmitting a copy of J through each arc, the cost of making a copy of J at each vertex and the number of copies of J needed at each vertex in N are defined. Definig a file transfer on N, we give a method for designing an optimal file transfer by which we mean a file transfer whose total cost of transmitting and making copies of J is minimum on N.

In a file transmission net N with vertex set V and arc set B, copies of a file J are distributed from a vertex to every vertex, subject to certain rules on file transmission. A cost of making one copy of J at each vertex µ is called a copying cost at µ, a cost of transmitting one copy of J through each arc (x, y) is called a transmission cost (x, y), and the number of copies of J demanded at each vertex u in N is called a copy demand at u. A scheduling of distributing copies of J from a vertex, say s, to every vertex on N is called a file transfer from s. The vertex s is called the source of the file transfer. A cost of a file transfer is defined, a file transfer from s is said to be optimal if its cost is not larger than the cost of any other file transfer from s, and an optimal file transfer from s is said to be optimum on N if its cost is not larger than that of an optimal file transfer from any other vertex. In this note, it is proved that an optimal file transfer from a vertex with a minimum copying cost is optimum on N, if there holds M U where M and U are the mother vertex set and the positive demand vertex set of N, respectively. Also it is shown by using an example that an optimal file transfer from a vertex with a minimum copying cost is not always optimum on N when M ⊃ U holds.

The demand for mobile communication services is rapidly increasing, because the mobile communication service is synonymy of an ideal communication style realizing communication in anytime, anywhere and with anyone. The development of economic and social activities is a primary factor of the increasing demand for mobile communication services. The demand stimulates the development of technology in mobile communication including personal communication services. Thus mobile communication has been one of the most active research in communications in the last several years. There exist various problems to which graph & network theory is applicable in mobile communication services (for example, channel assignment algorithm in cellular system, protocol in modile communication networks and traffic control in mobile communication ). A model of a cellular system has been formulated using a graph and it is known that the channel assignment problem is equivalent to the coloring problem of graph theory. Recently, two types of coloring problems on graphs or networks related to the channel assignment problem were proposed. Mainly, we introduce these coloring problems and show some results on these problems in this paper.

Analysis of waiting time to deliver a message M from a source S to a destination D is deeply related to connectivity analysis, which is an important issue in fundamental studies of mobile multi-hop networks. In [1], we compared the mean waiting times of two methods to deliver M with the mean value of the minimum waiting time. The mean minimum waiting time was obtained by computer simulation because theoretical analysis of this mean is not easy, although another two methods were analyzed theoretically. In this paper, we propose an approximate method to theoretically analyze the mean minimum waiting time in a one-dimensional street network, and show that this method gives a good approximation of the mean minimum waiting time. Also, we consider shadowing and change of directions of mobile nodes at intersections as negative factors arising in two-dimensional street networks. We extend the above method to compute the mean minimum waiting time considering these factors, and discuss how the mean minimum waiting time is affected by these factors.

In multi-hop wireless networks, communication quality depends on the selection of a path between source and destination nodes from several candidate paths. Exploring how path selection affects communication quality is important to characterize the best path. To do this, in [1], we used expected transmission count (ETX) as a metric of communication quality and theoretically characterized minimum route ETX, which is the ETX of the best path, in a static one-dimensional random multi-hop network. In this paper, we characterize minimum route ETX in static two-dimensional multi-hop networks. We give the exact formula of minimum route ETX in a two-dimensional network, assuming that nodes are located with lattice structure and that the ETX function satisfies three conditions for simplifying analysis. This formula can be used as an upper bound of minimum route ETX without two of the three conditions. We show that this upper bound is close to minimum route ETX by comparing it with simulation results. Before deriving the formula, we also give the formula for a one-dimensional network where nodes are located at constant intervals. We also show that minimum route ETX in the lattice network is close to that in a two-dimensional random network if the node density is large, based on a comparison between the numerical and simulation results.

A problem of synthesizing an optimal file transfer on a file transmission net N is to consider how to distribute, with a minimum total cost, copies of a file J with some information from source vertex set S to all vertices of N by the respective vertices' copy demand numbers. The case of |S| =1 has been studied so far. This paper deals with N such that |S|1, where a forest-type file transfer is defined. This paper proposes a polynomial time algorithm to synthesize an optimal forest-type file transfer on such N satisfying SM U, where M and U are mother vertex set and positive demand vertex set of N, respectively.

A problem of obtaining an optimal file transfer on a file transmission net N is to consider how to distribute, with a minimum total cost, copies of a file with some information from a vertex of N to all vertices of N by the respective vertices' copy demand numbers (i.i., needed numbers of copies). The maximum number of copies of file which can be made at a vertex is called the copying number of the vertex. In this paper, we consider as N an arborescence-net with constraints on copying numbers, and give a necessary and sufficient condition for a file transfer to be optimal on N, and furthermore propose an O(n2) algorithm for obtaining an optimal file transfer on N, where n is the number of vertices of N.

A vertex-capacitated network is a graph whose edges and vertices have infinite positive capacities and finite positive capacities, respectively. Such a network is a model of a communication system in which capacities of links are much larger than those of stations. This paper considers a problem of realizing a flow-saturation in an undirected vertex-capacitated network by adding the least number of edges. By defining a set of influenced vertex pairs by adding edges, we show the follwing results.(1) It suffices to add the least number of edges to unsaturated vertex pairs for realizing flow-saturation.(2) An associated graph of a flow-unsaturated network defined in this paper gives us a sufficient condition that flow-saturation is realized by adding a single edge.

Let G be a directed graph containing n nodes and m edges, with each edge of nonnegative length. Given two specified nodes s and t, the length of a k-tuple of edge-disjoint paths from s to t in G is the sum of the lengths of all the edges on these k paths. A polynomial time algorithm for finding a shortest k-tuple of edge-disjoint paths from s to t in G has been devised. Based on this algorithm, this paper considers the problem of finding a second shortest k-tuple of edge-disjoint paths from s to t in G, for which an O (min[n3, nm log n])-time is described.

This paper proposes a simple timing synchronization method in order to design a timing synchronization circuit with low-complex and low-volume digital signal processing (DSP) for orthogonal frequency division multiplexing (OFDM) packet transmission systems. The proposed method utilizes the subtraction process for acquirement of a timing metric of fast Fourier transform (FFT) window, whereas the conventional methods utilize the multiplication process. This paper adopts the proposed method to a standardized OFDM format, IEEE 802.11a, and elucidates that the proposed one shows good transmission performance as well as the conventional one in fast time-variant multi-path Rayleigh fading channels by computer simulation.

In a multihop network, radio packets are often relayed through inter-mediate stations (repeaters) in order to transfer a radio packet from a source to its destination. We consider a scheduling problem in a multihop network using a graphtheoretical model. Let D=(V,A) be the digraph with a vertex set V and an arc set A. Let f be a labeling of positive integers on the arcs of A. The value of f(u,v) means a frequency band assigned on the link from u to v. We call f antitransitive if f(u,v)f(v,w) for any adjacent arcs (u,v) and (v,w) of D. The minimum antitransitive-labeling problem is the problem of finding a minimum antitransitive-labeling such that the number of integers assigned in an antitransitive labeling is minimum. In this paper, we prove that this problem is NP-hard, and we propose a simple distributed approximation algorithm for it.

Dynamic Channel Assignment (DCA), which improves the efficiency of channel use in cellular mobile communication systems, requires finding an available channel for a new call after the call origination. This causes the delay which is defined as the time elapsing between call origination and completion of the channel search. For system planning, it is important to evaluate the delay characteristic of DCA because the delay corresponds to the waiting time of a call and influences service quality. It is, however, difficult to theoretically analyze the delay characteristics except its worst case behavior. The time delay of DCA has not been theoretically analyzed. The objective of this paper is analyzing the distribution and the mean value of the delay theoretically. The theoretical techniques in this paper are based on the techniques for analyzing the blocking rate performance of DCA.

The lower-bounded p-collection problem is the problem where to locate p sinks in a flow network with lower bounds such that the value of a maximum flow is maximum. This paper discusses the cover problems corresponding to the lower bounded p-collection problem. We consider the complexity of the cover problem, and we show polynomial time algorithms for its subproblems in a network with tree structure.

In a cellular system for mobile communications, every service area is divided into a number of cells for utilizing the frequency spectrum efficiently. Service areas for such systems are two dimensional, however, the analysis of the characteristics of the communication traffic for the areas are quite complicated, since the motion of the vehicles in the area can not be predicted precisely. For making the analysis easily, the areas are assumed to be band-shaped like a highway. Furthermore, in the analysis, the traffic offered to a cell is assumed to be stationary. In actual systems, the density of vehicles and the offered communication traffic is not stationary, so that many differences exist between the analysis and the actual systems. This paper presents an analysis method using state equations. The equations represent the transient characteristics of mobile communication traffic when a band-shaped service area is assumed. The transition is made by accidents or congestion, and causes the rapid offered traffic change in a communication system. In the method, numerical analysis is made under the consideration of "handoff" operation. The operation consists of surrendering the channel used in the previous cell and reassigning a new channel when the vehicle crosses the cell boundary. The analytical results are compared with the simulations, and the two results show good agreement. The method presented in this paper can be used for designing the switching system when the offered traffic changes rapidly due to accidents or congestion.

In a cellular mobile system, assigning a channel for a call in a cell so as to achieve high spectral efficiency is an important problem. In usual channel assignment for a cellular mobile system, a channel can be simultaneously assigned to some cells with a constant separation distance. This usual model of a cellular mobile system has been formulated using a graph and it is known that the channel assignment problem is equivalent to the coloring problem of graph theory. Recently, a new channel assignment scheme has been proposed. This scheme takes the degree of interference into consideration. In the scheme, a channel is simultaneously assigned if the CIR (carrier-to-interference ratio) is more than the desired value. In this paper, we formulate this new model using a network and a new coloring problem of networks. The new coloring problem of networks is a generalization of the usual coloring problem of graphs. One of the merits of this formulation is that the degree of cochannel interference between cells can be represented. In the usual formulation using a graph, the degree of cochannel interference between cells can not be represented. Therefore, spectral efficiency in the formulation using a network is higher than spectral efficiency in the formulation using a graph. In this paper, we show that the new coloring problem is an NP-hard problem. Subsequently, we rewrite the new coloring problem of networks to a coloring problem of graphs on some assumptions and consider the relation between the results on the new coloring and the results on the usual coloring.

Location theory on networks is concerned with the problem of selecting the best location in a specified network for facilities. Many studies for the theory have been done. However, few studies treat location problems on networks from the standpoint of measuring the closeness between two vertices by the capacity (maximum flow value) between two vertices. This paper concerns location problems, called covering problems on flow networks. We define two types of covering problems on flow networks. We show that covering problems on undirected flow networks and a covering problem on directed flow networks are solved in polynomial times.