Related papers: An Even Faster and More Unifying Algorithm for Com…
Suppose we label the vertices of a tree by positive integers. The weight of an edge is defined by a monotonically increasing function of the absolute value of the difference of the labels of its endpoints. We define the total cost of the…
Determining the interaction partners among protein/domain families poses hard computational problems, in particular in the presence of paralogous proteins. Available approaches aim to identify interaction partners among protein/domain…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.
We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the…
The Maximum Agreement Forest (Maf) problem is a well-studied problem in evolutionary biology, which asks for a largest common subforest of a given collection of phylogenetic trees with identical leaf label-set. However, the previous work…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
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…
Key agreement plays a crucial role in ensuring secure communication in public networks. Although algorithms developed many years ago are still being used, the emergence of quantum computing has prompted the search for new solutions. Tree…
Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have…