Related papers: Leafy Spanning Arborescences in DAGs

Bayesian networks, with structure given by a directed acyclic graph (DAG), are a popular class of graphical models. However, learning Bayesian networks from discrete or categorical data is particularly challenging, due to the large…

We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…

Sum-Product Networks with complex probability distribution at the leaves have been shown to be powerful tractable-inference probabilistic models. However, while learning the internal parameters has been amply studied, learning complex leaf…

Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the problem of finding in $D$ an out-branching with the minimum possible number of leaves, i.e., vertices of out-degree 0. Gutin, Razgon and Kim (2008) proved that…

We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…

We provide a structural description of, and invariants for, maximum spanning tree-packable graphs, i.e. those graphs G for which the edge connectivity of G is equal to the maximum number of edge-disjoint spanning trees in G. These graphs…

We study a distributed learning problem in which learning agents are embedded in a directed acyclic graph (DAG). There is a fixed and arbitrary distribution over feature/label pairs, and each agent or vertex in the graph is able to directly…

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…

Graph neural networks operate on graph-structured data via exchanging messages along edges. One limitation of this message passing paradigm is the over-squashing problem. Over-squashing occurs when messages from a node's expanded receptive…

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,…

We prove that every connected graph with $s$ vertices of degree~1 and 3 and $t$ vertices of degree at least~4 has a spanning tree with at least ${1\over 3}t +{1\over 4}s+{3\over 2}$ leaves. We present infinite series of graphs showing that…

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs…

Let $G$ be a connected graph in which almost all vertices have linear degrees and let $T$ be a uniform spanning tree of $G$. For any fixed rooted tree $F$ of height $r$ we compute the asymptotic density of vertices $v$ for which the…

A branch vertex in a tree is a vertex of degree at least three. We prove that, for all $s\geq 1$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch…

Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be…

The network coding problem asks whether data throughput in a network can be increased using coding (compared to treating bits as commodities in a flow). While it is well-known that a network coding advantage exists in directed graphs, the…

The connection between the maximum spanning tree in a directed graph and the best dependency tree of a sentence has been exploited by the NLP community. However, for many dependency parsing schemes, an important detail of this approach is…

Message passing neural networks iteratively generate node embeddings by aggregating information from neighboring nodes. With increasing depth, information from more distant nodes is included. However, node embeddings may be unable to…