Related papers: Edit Distance between Unrooted Trees in Cubic Time
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…
The edit distance $ed(X,Y)$ of two strings $X,Y\in \Sigma^*$ is the minimum number of character edits (insertions, deletions, and substitutions) needed to transform $X$ into $Y$. Its weighted counterpart $ed^w(X,Y)$ minimizes the total cost…
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…
The independence number of a tree decomposition is the maximum of the independence numbers of the subgraphs induced by its bags. The tree-independence number of a graph is the minimum independence number of a tree decomposition of it.…
We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…
In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in $O(n\log^2{n}\log\log{n})$ total time and explicitly maintains the set of…
The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…
Distance geometry explores the properties of distance spaces that can be exactly represented as the pairwise Euclidean distances between points in $\mathbb{R}^d$ ($d \geq 1$), or equivalently, distance spaces that can be isometrically…
Given access to the vertex set $V$ of a connected graph $G=(V,E)$ and an oracle that given two vertices $u,v\in V$, returns the shortest path distance between $u$ and $v$, how many queries are needed to reconstruct $E$? Firstly, we show…
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…
The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…
In this paper we describe a randomized algorithm which returns a maximal spanning forest of an unknown {\em weighted} undirected graph making $O(n)$ $\mathsf{CUT}$ queries in expectation. For weighted graphs, this is optimal due to a result…
We give an algorithm that computes a $(1+\epsilon)$-approximate Steiner forest in near-linear time $n \cdot 2^{(1/\epsilon)^{O(ddim^2)} (\log \log n)^2}$. This is a dramatic improvement upon the best previous result due to Chan et al., who…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
We present a dynamic data structure that maintains a tree decomposition of width at most $9k+8$ of a dynamic graph with treewidth at most $k$, which is updated by edge insertions and deletions. The amortized update time of our data…
We present an algorithm for approximating the edit distance $\operatorname{ed}(x, y)$ between two strings $x$ and $y$ in time parameterized by the degree to which one of the strings $x$ satisfies a natural pseudorandomness property. The…
A rearrangement operation makes a small graph-theoretical change to a phylogenetic network to transform it into another one. For unrooted phylogenetic trees and networks, popular rearrangement operations are tree bisection and reconnection…
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…