Related papers: Practical estimation of rotation distance and indu…
Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
Rotation distance between rooted binary trees is the minimum number of simple rotations needed to transform one tree into the other. Computing the rotation distance between a pair of rooted trees can be quickly reduced in cases where there…
It is an open question whether there exists a polynomial-time algorithm for computing the rotation distances between pairs of extended ordered binary trees. The problem of computing the rotation distance between an arbitrary pair of trees,…
Computing the rotation distance between two binary trees with $n$ internal nodes efficiently (in $poly(n)$ time) is a long standing open question in the study of height balancing in tree data structures. In this paper, we initiate the study…
As well known the rotation distance D(S,T) between two binary trees S, T of n vertices is the minimum number of rotations of pairs of vertices to transform S into T. We introduce the new operation of chain rotation on a tree, involving two…
Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we…
Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where…
We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at…
Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the…
This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…
We revisit the classical problem of searching in a binary search tree (BST) using rotations, and present novel connections of this problem to a number of geometric and combinatorial structures. In particular, we show that the execution…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…
Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its…
This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…
Motion Planning is necessary for robots to complete different tasks. Rapidly-exploring Random Tree (RRT) and its variants have been widely used in robot motion planning due to their fast search in state space. However, they perform not well…
In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a…