Signal compression is an important problem encountered in many applications. Various techniques have been proposed over the years for addressing the problem. In this paper, we present a time domain algorithm based on the coding of line segments which are used to approximate the signal. These segments are fit in a way that is optimal in the rate distortion sense. Although the approach is applicable to any type of signal, we focus, in this paper, on the compression of electrocardiogram (ECG) signals. ECG signal compression has traditionally been tackled by heuristic approaches. However, it has been demonstrated [1] that exact optimization algorithms outperform these heuristic approaches by a wide margin with respect to reconstruction error. By formulating the compression problem as a graph theory problem, known optimization theory can be applied in order to yield optimal compression. In this paper, we present an algorithm that will guarantee the smallest possible distortion among all methods applying linear interpolation given an upper bound on the available number of bits. Using a varied signal test set, extensive coding experiments are presented. We compare the results from our coding method to traditional time domain ECG compression methods, as well as, to more recently developed frequency domain methods. Evaluation is based both on percentage root-mean-square difference (PRD) performance measure and visual inspection of the reconstructed signals. The results demonstrate that the exact optimization methods have superior performance compared to both traditional ECG compression methods and the frequency domain methods.