Related papers: Optimal Random Matchings, Tours, and Spanning Tree…
We study the minimum spanning tree problem on the complete graph $K_n$ where an edge $e$ has a weight $W_e$ and a cost $C_e$, each of which is an independent copy of the random variable $U^\gamma$ where $\gamma\leq 1$ and $U$ is the uniform…
This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…
For an arbitrary tree we investigate the problems of constructing a maximum matching which minimizes or maximizes the cardinality of a maximum matching of the graph obtained from original one by its removal and present corresponding…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper,…
For a set of red and blue points in the plane, a minimum bichromatic spanning tree (MinBST) is a shortest spanning tree of the points such that every edge has a red and a blue endpoint. A MinBST can be computed in $O(n\log n)$ time where…
Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…
Considering the optimal alignment of two i.i.d. random sequences of length $n$, we show that when the scoring function is chosen randomly, almost surely the empirical distribution of aligned letter pairs in all optimal alignments converges…
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 study a tree coloring model introduced by Guidon (2018), initially based on an analogy with a remote control system of a rail yard, seen as switches on a binary tree. For a given binary tree, we formalize the constraints on the coloring,…
Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…
We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that…
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
Finding interactions between variables in large and high-dimensional datasets is often a serious computational challenge. Most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that…
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation,…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…