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The standard algorithms of decision trees and their derived methods are usually constructed on the basis of the frequency information. However, they still suffer from a dilemma or multichotomous question for continuous attributes when two or more candidate cut points have the same or similar splitting performance with the optimal value, such as the maximal information gain ratio or the minimal Gini index. In this paper, we propose a unified framework model to deal with this question. We then design two algorithms based on Splitting Performance and the number of Expected Segments, called SPES1 and SPES2, which determine the optimal cut point, as follows. First, several candidate cut points are selected based on their splitting performances being the closest to the optimal. Second, we compute the number of expected segments for each candidate cut point. Finally, we combine these two measures by introducing a weighting factor $\alpha $ to determine the optimal one from several candidate cut points. To validate the effectiveness of our methods, we perform them on 25 benchmark datasets. The experimental results demonstrate that the classification accuracies of the proposed algorithms are superior to the current state-of-the-art methods in tackling the multichotomous question, about 5% in some cases. In particular, according to the proposed methods, the number of candidate cut points converges to a certain extent.

Data offloading through vehicular ad hoc networks (VANETs) is one of the most promising methods for overcoming the overload problem in cellular networks. As data delivery by service providers consumes resources such as bandwidth, storage and power, the incentive scheme with the optimal pricing strategy must be identified. In the literature, most incentive schemes focus on offloading through fixed nodes, such as roadside units (RSUs). It remains very challenging to motivate a moving vehicle to help other users deliver their data due to the high mobility of vehicles. Game theory is a widely adopted method for analyzing pricing issues in wireless networks. Therefore, this paper proposes an optimal pricing strategy that uses the Stackelberg game to model the interaction between a service provider and a service requester. Then, the Stackelberg equilibrium is derived under the corresponding conditions. Next, an algorithm is proposed for selecting the service provider that offers the lowest price based on the results of the Stackelberg equilibrium. Finally, the simulation results demonstrate that the proposed algorithm can effectively reduce the downloading time of a task while maximizing the utilities of both the service provider and the requester.