Related papers: Dynamic subtrees queries revisited: the Depth Firs…
The dynamic trees problem is to maintain a forest undergoing edge insertions and deletions while supporting queries for information such as connectivity. There are many existing data structures for this problem, but few of them are capable…
Depth first search (DFS) tree is a fundamental data structure for solving various problems in graphs. It is well known that it takes $O(m+n)$ time to build a DFS tree for a given undirected graph $G=(V,E)$ on $n$ vertices and $m$ edges. We…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
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 dynamic trees problem is to maintain a tree under edge updates while supporting queries like connectivity queries or path queries. Despite the first data structure for this fundamental problem -- the link-cut tree -- being invented 40…
Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering…
Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
We present an algorithm for a fault tolerant Depth First Search (DFS) Tree in an undirected graph. This algorithm is drastically simpler than the current state-of-the-art algorithms for this problem, uses optimal space and optimal…
Depth first search (DFS) tree is a fundamental data structure for solving various graph problems. The classical DFS algorithm requires $O(m+n)$ time for a graph having $n$ vertices and $m$ edges. In the streaming model, an algorithm is…
The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
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…
As the sizes of graphs grow rapidly, currently many real-world graphs can hardly be loaded in the main memory. It becomes a hot topic to compute depth-first search (DFS) results, i.e., depth-first order or DFS-Tree, on semi-external memory…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this…
We present a dynamic data structure for representing a graph $G$ with tree-depth at most $D$. Tree-depth is an important graph parameter which arose in the study of sparse graph classes. The structure allows addition and removal of edges…
Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…