Related papers: Complexity Analysis of Balloon Drawing for Rooted …
From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the…
The construction of a dendogram on a set of individuals is a key component of a genomewide association study. However even with modern sequencing technologies the distances on the individuals required for the construction of such a…
We prove cyclic sieving phenomena satisfied by corner-rooted plane trees (alias ordered trees). The sets of rooted plane trees that we consider are: (1) all trees with $n$ nodes; (2) all trees with $n$ nodes and $k$ leaves; (3) all trees…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…
We consider the in-plane motion of elastic strings on tree-like network, observed from the 'leaves'. We investigate the inverse problem of recovering not only the physical properties i.e. the 'optical lengths' of each string, but also the…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
The protection number of a plane tree is the minimal distance of the root to a leaf; this definition carries over to an arbitrary node in a plane tree by considering the maximal subtree having this node as a root. We study the the…
The quality of a wood log in the wood industry depends heavily on the presence of both outer and inner defects, including inner knots that are a result of the growth of tree branches. Today, locating the inner knots require the use of…
We define the \emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to…
There is a rising interest in mapping trees using satellite or aerial imagery, but there is no standardized evaluation protocol for comparing and enhancing methods. In dense canopy areas, the high variability of tree sizes and their spatial…
We consider the wavelet transform of a finite, rooted, node-ranked, $p$-way tree, focusing on the case of binary ($p = 2$) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
This paper studies the "explanation problem" for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A whose…
In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier. These regularites admit two different types of behavior and in this work we investigate which…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by DAG compression. A method for quantifying the degree of self-similarity of plants through self-nested trees has been…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
This survey reviews Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a ribbon, and the ribbonlength problem asks to minimize the…