On Length-Sensitive Fréchet Similarity.

Taking length into consideration while comparing 1D shapes is a challenging task. In particular, matching equal-length portions of such shapes regardless of their combinatorial features, and only based on proximity, is often required in biomedical and geospatial applications. In this work, we define the length-sensitive partial Fréchet similarity (LSFS) between curves (or graphs), which maximizes the length of matched portions that are close to each other and of equal length. We present an exact polynomial-time algorithm to compute LSFS between curves under L 1 and L ∞ . For geometric graphs, we show that the decision problem is NP-hard even if one of the graphs consists of one edge.