## 1 Introduction
For example, long-term sensor data loss in an ocean-area contamination disaster impedes not only the cause and origin identification of the contamination but also the analysis of its dissemination progress and pollution area. Successively, such blockings prevent humankind from the prediction and prevention of the future disasters and their movements [19; 20; 21; 22]. Ultimately, the sensor data lossless preservation for long-term communication failure in the previous disaster is certainly helpful for us to predict and prevent the same or similar future disasters, even though we fail in the real-time monitoring and controlling for the current disaster. Insufficient memory capacity of a sensor node, however, makes it impossible to save the entire sensor data set lost during a long-term communication failure. Therefore, it is necessary to minimize the loss of the original sensor data during communication failure and to restore the lost sensor data nearly to the level of the original sensor data after the communication failure recovery. In other words, we need a method to reduce the sensor data loss caused by the memory capacity limit of the sensor node during communication failure. To date, only a few such methods, including _winavg_[23], _delta_[23], _CQP_[24], and _2 MC_[19; 20] have been proposed. These methods use compression to replace two or more consecutive sensor data with an average value as a representative or to select a representative between two or three consecutive sensor data. All the sensor data apart from the representatives become lost in these methods. The remaining representatives are transmitted to the destination site, where the lost sensor data are recovered to these representatives (in _winavg_) or to the values interpolated using them. Most of these methods, however, do not show good performance in the average error rate as a measure of the data loss because these use their own very simple rules without consideration for performance measures such as that average error rate. The _2 MC_ method shows much better performance than _winavg_, _delta_, and _CQP_ methods in the sensor data loss minimization, because this method uses an error rate as a performance measure in selecting representatives. However, since the _2 MC_ method can fail to find the absolute positions of the lost sensor data, it has fatal drawback of being unable to recover the lost sensor data. Moreover, even though a communication framework for using these methods in wireless sensor networks is necessary, no framework for this has been presented. Against this background, in this paper, we propose a framework to reduce sensor data loss during communication failures and we present a formal approach for the Selection by Minimum Error and Pattern (SMEP) method that plays the most important role in the reduction of sensor data loss in the proposed framework. The SMEP method uses a line interpolation error measure in selecting representatives to minimize errors in recovering lost sensor data. Compared with other methods using real-field sensor data sets, the experimental results show that the SMEP method has a much better average error rate within up to 87.5% sensor data loss (that is, 12.5% compression ratio). The SMEP method is also feasible, in that it can recover all lost sensor data. The remainder of this paper is organized as follows. In Section 2, we introduce related works on technologies for sensor data compression, including _winavg_[23], _delta_[23], _CQP_[24], and 2_MC_[19; 20], which are mostly applicable for sensor data loss reduction in sensor networks. Section 3 proposes a communication framework for the reduction of sensor data loss during communication failures. The proposed SMEP method can be applied to this framework, playing an important role. In Section 4, the fundamental formal definitions and properties of sensor data, compression interval, and round compression are introduced. These are necessary to introduce the SMEP method.