Given a tree T with weight and length on each edge, as well as a lower bound L and an upper bound U , the so-called length-constrained maximum-density subtree problem is to find a maximum-density subtree in T such that the length of this subtree is between L and U . In this study, we present an algorithm that runs in O(nU log n) time for the case when the edge lengths are positive integers, whe...

We give a counterexample to the conjecture of Martin and Thatte that two balanced rooted binary leaf-labelled trees on $n$ leaves have maximum agreement subtree (MAST) size at least $n^{\frac{1}{2}}$. In particular, we show for any $c>0$, there exist such MAST these has less than $c n^{\frac{1}{2}}$. also improve lower bound $n^{\frac{1}{6}}$.

The Weisfeiler-Lehman (WL) test is a widely used algorithm in graph machine learning, including kernels, metrics, and neural networks. However, it focuses only on the consistency of graph, which means that unable to detect slight structural differences. Consequently, this limits its ability capture information, also performance existing models rely WL test. This limitation particularly severe f...

This paper considers the approximability of the largest common subtree and the largest common subgraph problems, which have applications in molecular biology. It is shown that approximating the problems within a factor of n is NP-complete, while a general search algorithm which approximates both problems within a factor of O(n= logn) is presented. Moreover, several variants of the largest commo...