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The profile-based matching problem is the problem of finding a matching that optimizes profile from an instance $(G, r, \langle u_1, \dots, u_r \rangle)$, where $G$ is a bipartite graph $(A \cup B, E)$, $r$ is the number of utility…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
The general communication tree embedding problem is the problem of mapping a set of communicating terminals, represented by a graph G, into the set of vertices of some physical network represented by a tree T. In the case where the vertices…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…
The tree edit distance (TED) between two rooted ordered trees with $n$ nodes labeled from an alphabet $\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of valid operations consisting of insertions, deletions…
This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\it minimum normalized cuts}/{\it isoperimteric…
The Rooted Maximum Leaf Outbranching problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic…
The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…
It is known that the size of the largest common subtree (i.e., the maximum agreement subtree) of two independent random binary trees with $n$ given labeled leaves is of order between $n^{0.366}$ and $n^{1/2}$. We improve the lower bound to…
We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-independence number. In [Dallard, Milani\v{c}, and…
We consider the classical tree edit distance between ordered labeled trees, which is defined as the minimum-cost sequence of node edit operations that transform one tree into another. The state-of-the-art solutions for the tree edit…
Given a weighted bipartite graph $G = (L, R, E, w)$, the maximum weight matching (MWM) problem seeks to find a matching $M \subseteq E$ that maximizes the total weight $\sum_{e \in M} w(e)$. This paper presents a novel algorithm with a time…
Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…
We study the topmost weight matrix of neural network language models. We show that this matrix constitutes a valid word embedding. When training language models, we recommend tying the input embedding and this output embedding. We analyze…