Related papers: Optimal Unimodular Matching
For an additive submonoid $\mathcal{M}$ of $\mathbb{R}_{\ge 0}$, the weight of an $\mathcal{M}$-labeled directed graph is the sum of all of its edge labels, while the content is the product of the labels. Having fixed $\mathcal{M}$ and a…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…
We present new and improved fixed-parameter algorithms for computing maximum agreement forests (MAFs) of pairs of rooted binary phylogenetic trees. The size of such a forest for two trees corresponds to their subtree prune-and-regraft…
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;…
We consider a weighted counting problem on matchings, denoted $\textrm{PrMatching}(\mathcal{G})$, on an arbitrary fixed graph family $\mathcal{G}$. The input consists of a graph $G\in \mathcal{G}$ and of rational probabilities of existence…
It is well known that finding extremal values and structures can be hard in weighted graphs. However, if the weights are random, this problem can become way easier. In this paper, we examine the minimal weight of a union of $k$…
We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
This paper presents a unified analysis framework that captures recent advances in the study of local-optimality characterizations for codes on graphs. These local-optimality characterizations are based on combinatorial structures embedded…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
Several studies have shown that combining machine learning models in an appropriate way will introduce improvements in the individual predictions made by the base models. The key to make well-performing ensemble model is in the diversity of…
Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
In this work, we present an $\Omega\left(\min\{\log \Delta, \sqrt{\log n}\}\right)$ lower bound for Maximal Matching (MM) in $\Delta$-ary trees against randomized algorithms. By a folklore reduction, the same lower bound applies to Maximal…
We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…