Related papers: Tree Drawings with Columns
This paper presents a novel algorithm, called MRRT, which uses multiple rapidly-exploring random trees for fast online replanning of autonomous vehicles in dynamic environments with moving obstacles. The proposed algorithm is built upon the…
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
In an upward planar 2-slope drawing of a digraph, edges are drawn as straight-line segments in the upward direction without crossings using only two different slopes. We investigate whether a given upward planar digraph admits such a…
Rapidly Exploring Random Trees (RRT) is one of the most widely used algorithms for motion planning in the field of robotics. To reduce the exploration time, RRT-Connect was introduced where two trees are simultaneously formed and eventually…
Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…
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…
Supertree construction is the process by which a set of phylogenetic trees, each on a subset of the overall set X of species, is combined into a tree on the full set S. The traditional use of supertree methods is the assembly of a large…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
Trees can accelerate queries that search or aggregate values over large collections. They achieve this by storing metadata that enables quick pruning (or inclusion) of subtrees when predicates on that metadata can prove that none (or all)…
Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…
We consider the problem of drawing multiple gene trees inside a single species tree in order to visualize multispecies coalescent trees. Specifically, the drawing of the species tree fills a rectangle in which each of its edges is…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…
Designing fare systems for public transportation networks is a challenging task. A popular approach is to partition the network into fare zones (``zoning'') and fix journey prices depending on the number of traversed zones (``pricing''). In…
We introduce top trees as a design of a new simpler interface for data structures maintaining information in a fully-dynamic forest. We demonstrate how easy and versatile they are to use on a host of different applications. For example, we…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
The slope number of a graph $G$ is the smallest number of slopes needed for the segments representing the edges in any straight-line drawing of $G$. It serves as a measure of the visual complexity of a graph drawing. Several bounds on the…
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…
We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms…