Related papers: Dynamic DFS Tree in Undirected Graphs: breaking th…
The three-in-a-tree problem is to determine if a simple undirected graph contains an induced subgraph which is a tree connecting three given vertices. Based on a beautiful characterization that is proved in more than twenty pages,…
It is shown that a breadth-first search in a directed or undirected graph with $n$ vertices and $m$ edges can be carried out in $O(n+m)$ time with $n\log_2 3+O((\log n)^2)$ bits of working memory.
The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of…
In the CONGEST model, a communications network is an undirected graph whose $n$ nodes are processors and whose $m$ edges are the communications links between processors. At any given time step, a message of size $O(\log n)$ may be sent by…
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…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Depth-first search (DFS) is the basis for many efficient graph algorithms. We introduce general techniques for the efficient implementation of DFS-based graph algorithms and exemplify them on three algorithms for computing strongly…
In many real datasets such as social media streams and cyber data sources, graphs change over time through a graph update stream of edge insertions and deletions. Detecting critical patterns in such dynamic graphs plays an important role in…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
Motivated by recent applications of dominator computations, we consider the problem of dynamically maintaining the dominators of flow graphs through a sequence of insertions and deletions of edges. Our main theoretical contribution is a…
This paper addresses the problem of designing a {\em fault-tolerant} $(\alpha, \beta)$ approximate BFS structure (or {\em FT-ABFS structure} for short), namely, a subgraph $H$ of the network $G$ such that subsequent to the failure of some…
Graph searches and their respective search trees are widely used in algorithmic graph theory. The problem whether a given spanning tree can be a graph search tree has been considered for different searches, graph classes and search tree…
Given an undirected, anonymous, port-labeled graph of $n$ memory-less nodes, $m$ edges, and degree $\Delta$, we consider the problem of dispersing $k\leq n$ robots (or tokens) positioned initially arbitrarily on one or more nodes of the…
Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms. While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little…
Blocking flows, introduced by Dinic [2] for network flow, have been used to speed up many augmenting-path type algorithms, especially matching algorithms e.g., [18, 23, 16]. We present an $O(m)$ time algorithm for blocking trails for…
We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…
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…
A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E) encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can be iteratively constructed by n-1 maximum flow computations. They solve the multiterminal…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…
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…