Before revision:   To demonstrate that techniques developed under  LCS(-like) measurements are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.
After revision:  For a given pair of time series of length n such that the dissimilarity between any elements is an integer between zero and c, we propose an integer sequence that represents any substring-substring DTW distance as its band-substring LIS length. The length of the produced integer sequence is O(c n^2), which can be translated to O(n^2) for constant dissimilarity functions. To demonstrate that techniques developed under LCS(-like) measurements are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.