Related papers: Equal Splits of Vertex-Weighted Trees
In this draft we prove an interesting structural property related to the problem of computing {\em all the best swap edges} of a {\em tree spanner} in unweighted graphs. Previous papers show that the maximum stretch factor of the tree where…
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…
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…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…
The graph parameter vertex integrity measures how vulnerable a graph is to a removal of a small number of vertices. More precisely, a graph with small vertex integrity admits a small number of vertex removals to make the remaining connected…
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…
A gluing of two rooted trees is an identification of their leaves and un-subdivision of the resulting 2-valent vertices. A gluing of two rooted trees is subdivergence free if it has no 2-edge cuts with both roots on the same side of the…
Machine learning algorithms aim at minimizing the number of false decisions and increasing the accuracy of predictions. However, the high predictive power of advanced algorithms comes at the costs of transparency. State-of-the-art methods,…
In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
We propose the first branch-&-price algorithm for the maximum agreement forest problem on unrooted binary trees: given two unrooted X-labelled binary trees we seek to partition X into a minimum number of blocks such that the induced…
Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…
This paper addresses the following questions for a given tree $T$ and integer $d\geq2$: (1) What is the minimum number of degree-$d$ subtrees that partition $E(T)$? (2) What is the minimum number of degree-$d$ subtrees that cover $E(T)$? We…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Graphs with bounded treewidth and bounded maximum degree are known to have tree-partitions of bounded width. What can be said if the bounded treewidth assumption is strengthened to bounded pathwidth? We prove that every graph with bounded…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to…