We consider a compound problem of the generalized minimum-cost flow problem and the independent-flow problem, which we call the generalized independent-flow problem. The generalized minimum-cost flow problem is to find a minimum-cost flow in a capacitated network with gains, where each arc flow is multiplied by a gain factor when going through an arc. On the other hand, the independent-flow problem due to Fujishige is to find a minimum-cost flow in a multiple-source multiple-sink capacitated network with submodular constraints on the set of supply vectors on the source vertex set and on the set of demand vectors on the sink vertex set. We present a polynomial-time algorithm for the generalized independent-flow problem, based on Wayne's algorithm for generalized minimum-cost flows and Fujishige's algorithm for independent flows, which can be regarded as an extension of Wallacher and Zimmermann's submodular flow algorithm.

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The concepts of M-convex functions and M^〓-convex functions play central roles in the theory of discrete convex analysis which has been applied to mathematical economics. On the other hand, substitutability, which is a key property guaranteeing the existence of a stable matching in generalized stable marriage models, is known as a nice property in mathematical economics. In this paper, we introduce new properties, which are extensions of substitutability, and present new characterizations of M^〓-convex set functions by these properties.

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This paper studies a spatial duopoly model where customers are located at nodes and the demand functions are given for each node. For any fixed location of two firms, we analyze Bertrand-Nash equilibrium and derive a necessary and sufficient condition for the existence of equilibrium. We present an algorithm to compute all equilibria, provided profit functions have a finite number of peaks. The algorithm terminates within polynomial time if the number of peaks is polynomial in the number of nodes.

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There are demands for secure group communication on the internet, such as pay-per-view type broadcasting, business confidential information sharing and teleconference. Secure communication inside a groups on an open network is critical to enhance the internet capability. The public key system is not sufficient to support the group security, since it is not scalable for large groups. Some researchers propose a scalable group security model, managing several common keys for encryption and decryption sharing inside the community. In this paper, we will evaluate the performance of these group security model. Using M/G/∞ queueing models and the basic queueing theory, we show how to find the optimal condition of the allocation of the common keys if the joins to group is a Poisson process. In addition, we show our optimal condition may work for more general arrival processes by using the cross covariance formula (a variant of Papangelou's formula) for the stochastic intensity of departure process.

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An antenna of phased array radar (PAR) consists of a large number of individual radiating elements and steers its electromagnetic wave direction by shifting wave phases of these elements. Failed elements have to be detected, diagnosed, localized and replaced at scheduled times to hold a required performance of a radar system. However, the maintenance of an antenna should not be made so frequently, because it interrupts the radar operation and degrades the radar availability. This paper considers two typical policies of cyclic and delayed maintenances for a PAR where a certain number of survival elements is needed to hold a required performance : Failed elements in cyclic maintenance are replaced at periodic times, and they in delayed maintenance are done when their number has exceeded a predesignated one. When failures of a PAR antenna elements occur at a Poisson process, the expected costs are obtained and optimal policies for two maintenances which minimize them are analytically discussed.

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