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Pairwise compatibility graphs (PCGs) with non-negative integer edge weights recently have been used to describe rare evolutionary events and scenarios with horizontal gene transfer. Here we consider the case that vertices are separated by…
Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the…
Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection ($TBR$), subtree prune and regraft ($SPR$) and rooted subtree prune and regraft ($rSPR$). For a…
Billey et al. [arXiv:1507.04976] have recently discovered a surprisingly simple formula for the number $a_n(\sigma)$ of leaf-labelled rooted non-embedded binary trees (also known as phylogenetic trees) with $n\geq 1$ leaves, fixed (for the…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
Deciding whether a collection of unrooted trees is compatible is a fundamental problem in phylogenetics. Two different graph-theoretic characterizations of tree compatibility have recently been proposed. In one of these, tree compatibility…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
A graph $G=(V,E)$ with a vertex set $V$ and an edge set $E$ is called a pairwise compatibility graph (PCG, for short) if there are a tree $T$ whose leaf set is $V$, a non-negative edge weight $w$ in $T$, and two non-negative reals…
We address here spanning tree problems on a graph with binary edge weights. For a general weighted graph the minimum spanning tree is solved in super-linear running time, even when the edges of the graph are pre-sorted. A related problem,…
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…
We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…
This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…
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 give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree…
The Minimum Spanning Tree with Conflicting Edge Pairs is a generalization that adds conflict constraints to a classical optimization problem on graphs used to model several real-world applications. In the last few years several approaches,…
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 $X$…