University of TehranJournal of Algorithms and Computation2476-277653120210601Fr'echet-Like Distances between Two Rooted Trees11281145ENElenaFarahbakhsh 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