相关论文: A tight kernel for computing the tree bisection an…
The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this…
Given access to the vertex set $V$ of a connected graph $G=(V,E)$ and an oracle that given two vertices $u,v\in V$, returns the shortest path distance between $u$ and $v$, how many queries are needed to reconstruct $E$? Firstly, we show…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
The minimal number of rooted subtree prune and regraft (rSPR) operations needed to transform one phylogenetic tree into another one induces a metric on phylogenetic trees - the rSPR-distance. The rSPR-distance between two phylogenetic trees…
Phylogenetic networks provide a more general description of evolutionary relationships than rooted phylogenetic trees. One way to produce a phylogenetic network is to randomly place $k$ arcs between the edges of a rooted binary phylogenetic…
Performing efficient inference on Bayesian Networks (BNs), with large numbers of densely connected variables is challenging. With exact inference methods, such as the Junction Tree algorithm, clustering complexity can grow exponentially…
'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…
For a non-negative integer $\ell$, the $\ell$-leaf power of a tree $T$ is a simple graph $G$ on the leaves of $T$ such that two vertices are adjacent in $G$ if and only if their distance in $T$ is at most $\ell$. We provide a polynomial…
Tree size ($\rm{TS}$) is an interesting measure of complexity for multiqubit states: not only is it in principle computable, but one can obtain lower bounds for it. In this way, it has been possible to identify families of states whose…
Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…
Constrained Forest Problems (CFPs) as introduced by Goemans and Williamson in 1995 capture a wide range of network design problems with edge subsets as solutions, such as Minimum Spanning Tree, Steiner Forest, and Point-to-Point Connection.…
A normal network is uniquely determined by the set of phylogenetic trees that it displays. Given a set $\mathcal{P}$ of rooted binary phylogenetic trees, this paper presents a polynomial-time algorithm that reconstructs the unique binary…
Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Tree-child networks are an important class of phylogenetic network used to model reticulate evolutionary processes. These networks have attracted increasing attention from researchers with interests in both combinatorics and algorithms. A…
In molecular systematics, evolutionary trees are reconstructed from sequences at the tips under simple models of site substitution. A central question is how much sequence data is required to reconstruct a tree accurately? The answer…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
A soft tree is an actively studied variant of a decision tree that updates splitting rules using the gradient method. Although soft trees can take various architectures, their impact is not theoretically well known. In this paper, we…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…