DAIHINMIN, which means Grand Pauper, is a popular playing-card game in Japan. TANHINMIN is a simplified variant of DAIHINMIN, which was proposed by Nishino in 2007 in order to investigate the mathematical properties of DAIHINMIN. In this paper, we consider a 2-player generalized TANHINMIN, where the deck size is arbitrary n. We present a linear-time algorithm that determines which player has a winning strategy after all cards are distributed to the players.

A new edge-coloring algorithm for bipartite graphs is presented. This algorithm, based on the framework of the O(m log d + (m/d) log (m/d) log d) algorithm by Makino-Takabatake-Fujishige and the O(m log m) one by Alon, finds an optimal edge-coloring of a bipartite graph with m edges and maximum degree d in O(m log d + (m/d) log (m/d)) time. This algorithm does not require elaborate data structures, which the best known O(m log d) algorithm due to Cole-Ost-Schirra depends on.

In this study, we propose an object-based multimedia model for specifying the QoS (quality of service) requirements, such as the maximum data-dropping rate or the maximum data-delay rate. We also present a resource allocation model, called the net-profit model, in which the satisfaction of user's QoS requirements is measured by the benefit earned by the system. Based on the net-profit model, the system is rewarded if it can allocate enough resources to a multimedia delivery request and fulfill the QoS requirements specified by the user. At the same time, the system is penalized if it cannot allocate enough resources to a multimedia delivery request. We first investigate the problem of how to allocate resources efficiently, so that the QoS satisfaction is maximized. However, the net-profit may be distributed unevenly among the multimedia delivery requests. Thus, the second problem discusses how to allocate the resource efficiently so that the net-profit difference is minimized between any two multimedia requests. A dynamic programming based algorithm is proposed to find such an optimal solution with the minimum net-profit differences.