This paper introduces a new dimensionality reduction technique called Adaptive Piecewise Constant Approximation (APCA) for indexing large time series databases. APCA approximates each time series by a set of constant-value segments of varying lengths, minimizing individual reconstruction errors. The authors demonstrate that APCA can be indexed using multidimensional index structures and propose two distance measures: a lower bounding Euclidean distance approximation and a non-lower bounding but tight Euclidean distance approximation. These measures support fast exact and approximate searching. The paper compares APCA with other techniques theoretically and empirically, showing its superiority in terms of efficiency and accuracy. The main contributions include the development of APCA, its indexing method, and the proposed distance measures, which significantly improve the performance of similarity search in large time series databases.This paper introduces a new dimensionality reduction technique called Adaptive Piecewise Constant Approximation (APCA) for indexing large time series databases. APCA approximates each time series by a set of constant-value segments of varying lengths, minimizing individual reconstruction errors. The authors demonstrate that APCA can be indexed using multidimensional index structures and propose two distance measures: a lower bounding Euclidean distance approximation and a non-lower bounding but tight Euclidean distance approximation. These measures support fast exact and approximate searching. The paper compares APCA with other techniques theoretically and empirically, showing its superiority in terms of efficiency and accuracy. The main contributions include the development of APCA, its indexing method, and the proposed distance measures, which significantly improve the performance of similarity search in large time series databases.