We introduce the distance between two edges in a graph (nondirected graph) as the minimum number of edges in a tieset with the two edges. Using the distance between edges we define the eccentricity ετ (ej) of an edge ej. A finite nonempty set J of positive integers (no repetitions) is an eccentric set if there exists a graph G with edge set E such that ετ (ej) J for all ei E and each positive integer in J is ετ (ej) for some ej E. In this paper, we give necessary and sufficient conditions for a set J to be eccentric.

The concept of wireless ad hoc networking has unique features in which neither base stations nor wired backbone networks are required and a mobile node can communicate with a partner beyond the transmission range by multihopping. In this paper, innovations and issues in ad hoc network technologies are reviewed. The concept of a general-purpose ad hoc network is identified as a step toward next-generation ad hoc network development. The concept of an open community network is then presented as a vision for general-purpose ad hoc networks. An open community network is a novel information infrastructure for local communities based on wireless multihopping technologies, which may support an advanced information-oriented society in the twenty-first century. As a case study, an experimental system using PHS (Personal Handy Phone System) is described and some research issues for developing an open community network are identified.

It is of significantly importance in relation to the problem of diagnosis of deviation faults in linear analog circuits to check whether or not it is possible to uniquely determine the element-values in a given linear analog circuit from the node-voltage measurements at its accessible nodes and then of giving a method for actual computation of the element-values if it is possible, under the assumption that i) the circuit is of known topology (and of known element-kinds if possible) and ii) the actual value of each element-value of the circuit almost always deviates from the design value and is not known exactly. In this paper, the problem of checking the unique determinability of the element-values is called the element-value determinability problem, and its solutions which have been obtained until now are reviewed in perspectives to designing a publicly available user-oriented analog circuit diagnosis system.

Wireless network systems introducing both of the cellular concept and the ad-hoc concept have been proposed. Communication between two nodes in a cell is guaranteed by relaying capability of the base station in these systems. Additionally, two nodes can directly communicate with each other while they are close to each other. We call this type of network a two-hop wireless network. The teletraffic performance of this network depends on various parameters such as the size of a cell, location of nodes, the communication range of nodes, channel assignment schemes, teletraffic behavior and so on. The purpose of this paper is to theoretically analyze the teletraffic performance of the network, which has been evaluated by computer simulation, by introducing a simple model. This paper shows a technique to analyze the performance in this model. Also, this paper considers the range in which the two-hop wireless network works well for the efficient use of channels.

A problem of obtaining an optimal file transfer of a file transmission net N is to consider how to transmit, with the minimum total cost, copies of a certain file of information from some vertices, called sources, to other vertices of N by the respective vertices' copy demand numbers. This problem is NP-hard for a general file transmission net N. Some classes of N, on each of which a polynomial time algorithm for obtaining an optimal file transfer can be designed, are known. In the characterization, we assumed that file given originally to the source remains at the source without being transmitted. In this paper, we relax the assumption to the one that a sufficient number of copies of the file are given to the source and those copies can be transmitted from the source to other vertices on N. Under this new assumption, we characterize a class of file transmission nets, on each of which a polynomial time algorithm for obtaining an optimal file transfer can be designed. A minimum spanning tree with degree constraints plays a key role in the algorithm.

A problem of obtaining an optimal file transfer on a file transmission net N is to consider how to transmit, with a minimum total cost, copies of a certain file of information from some vertices to others on N by the respective vertices' copy demand numbers. This problem is NP-hard for a general file transmission net. So far, some class of N on which polynomial time algorithms for obtaining an optimal file transfer are designed has been known. In addition, if we deal with restricted file transfers, i. e. , forest-type file transfers, we can obtain an optimal 'forest-type' file transfer on more general class of N. This paper proves that for such general nets it suffices to consider forest-type file transfers in order to obtain an optimal file transfer.

This paper describes communication traffic characteristics in cellular systems employing the concept of reuse partitioning and Dynamic Channel Assignment. Such systems hava a problem of the spatial unbalance of blocking probability. The objective of this paper is overcoming this problem. To accomplish this objective, we use a method for analyzing communication traffic characteristics. We also show results on traffic characteristics in the systems.

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. We have studied location theory from the standpoint of measuring the closeness between two vertices by the capacity (maximum flow value) between two vertices. In a previous paper, we have considered location problems, called covering problems and proposed polynomial time algorithms for these problems. These problems are applicable to assigning files to some computers in a computer network. This paper is concerned with a covering problem called the single cover problem defined in the previous paper. First, we define a generalized single cover problem and show that an algorithm proposed in the previous paper can be applicable to solving the generalized single cover problem. Then, we define a single cover problem satisfying cardinality constrains and show that the problem is solved in a polynomial time.