University of TehranJournal of Algorithms and Computation2476-277653120210601Fr'echet-Like Distances between Two Rooted Trees1128114510.22059/jac.2021.81145ENElenaFarahbakhsh TouliStockholm University, Department of MathematicsJournal Article20210508The purpose of this paper is to extend the definition of Fr'echet distance which measures the distance between two curves to a distance (Fr'echet-Like distance) which measures the similarity between two rooted trees.<br />In this paper, I prove that the Fr'echet-Like distance between two trees is SNP-hard to compute.<br /> Later, I modify the definition of Fr'echet-Like distance to measure the distance between two merge trees, and I prove the relation between the interleaving distance and the modified Fr'echet-Like distance.https://jac.ut.ac.ir/article_81145_9cd801c5f8020bd4f3d182de4877a405.pdf