scholarly journals Space-Efficient Fully Dynamic DFS in Undirected Graphs †

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 52 ◽  
Author(s):  
Kengo Nakamura ◽  
Kunihiko Sadakane
Keyword(s):  
Undirected Graph ◽  
Undirected Graphs ◽  
Edge Connectivity ◽  
Worst Case ◽  
Depth First Search ◽  
Insertions And Deletions ◽  
Adjacency List ◽  
Graph Traversal ◽  
Dynamic Connectivity ◽  
Traversal Algorithm

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions.

scholarly journals Exploring graph traversal algorithms in graph-based molecular generation

2021 ◽  
Author(s):  
Rocío Mercado ◽  
Esben Bjerrum ◽  
Ola Engkvist
Keyword(s):  
Natural Products ◽  
Search Algorithm ◽  
Molecular Graph ◽  
Molecular Shape ◽  
Generative Models ◽  
Training Data ◽  
Depth First Search ◽  
Graph Traversal ◽  
The Impact ◽  
Traversal Algorithm

Here we explore the impact of different graph traversal algorithms on molecular graph generation. We do this by training a graph-based deep molecular generative model to build structures using a node order determined via either a breadth- or depth-first search algorithm. What we observe is that using a breadth-first traversal leads to better coverage of training data features compared to a depth-first traversal. We have quantified these differences using a variety of metrics on a dataset of natural products. These metrics include: percent validity, molecular coverage, and molecular shape. We also observe that using either a breadth- or depth-first traversal it is possible to over-train the generative models, at which point the results with the graph traversal algorithm are identical

Connectivity

2013 ◽  
pp. 37-47
Author(s):  
Mahtab Hosseininia ◽  
Faraz Dadgostari
Keyword(s):  
Connected Graph ◽  
Directed Graphs ◽  
Graph Connectivity ◽  
Breadth First Search ◽  
Undirected Graphs ◽  
Vertex Connectivity ◽  
Edge Connectivity ◽  
Graph Traversal ◽  
Path Component ◽  
Block Tree

In this chapter, the concept of graph connectivity is introduced. In the first section, some concepts such as walk, path, component and connected graph are defined, and connectedness of a graph from the viewpoint of vertex connectivity, and also, edge connectivity are discussed. Then, blocks and block tree of graphs are illustrated. In addition, connectivity in directed graphs is introduced. Furthermore, in the last section, two graph traversal algorithms, depth first search and breadth first search, are described to investigate the connectedness of directed and undirected graphs.

AN EFFICIENT DISTRIBUTED ALGORITHM FOR 3-EDGE-CONNECTIVITY

2006 ◽  
Vol 17 (03) ◽  
pp. 677-701 ◽  
Author(s):  
YUNG H. TSIN
Keyword(s):  
Distributed Algorithm ◽  
Computer Network ◽  
Connected Components ◽  
Message Complexity ◽  
Edge Connectivity ◽  
Worst Case ◽  
Dense Networks

A distributed algorithm for finding the cut-edges and the 3-edge-connected components of an asynchronous computer network is presented. For a network with n nodes and m links, the algorithm has worst-case [Formula: see text] time and O(m + nhT) message complexity, where hT < n. The algorithm is message optimal when [Formula: see text] which includes dense networks (i.e. m ∈ Θ(n2)). The previously best known distributed algorithm has a worst-case O(n3) time and message complexity.

Two Streamlined Depth-First Search Algorithms

1986 ◽  
Vol 9 (1) ◽  
pp. 85-94
Author(s):  
Robert Endre Tarjan
Keyword(s):  
Directed Graph ◽  
Graph Algorithms ◽  
Undirected Graph ◽  
Linear Time ◽  
Search Algorithms ◽  
Depth First Search ◽  
Time Graph

Many linear-time graph algorithms using depth-first search have been invented. We propose simplified versions of two such algorithms, for computing a bipolar orientation or st-numbering of an undirected graph and for finding all feedback vertices of a directed graph.

scholarly journals Time-Space Tradeoffs for Undirected Graph Traversal by Graph Automata

1996 ◽  
Vol 130 (2) ◽  
pp. 101-129 ◽  
Author(s):  
Paul Beame ◽  
Allan Borodin ◽  
Prabhakar Raghavan ◽  
Walter L. Ruzzo ◽  
Martin Tompa
Keyword(s):  
Undirected Graph ◽  
Graph Traversal ◽  
Time Space

Undirected Graphs Realizable as Graphs of Modular Lattices

1965 ◽  
Vol 17 ◽  
pp. 923-932 ◽  
Author(s):  
Laurence R. Alvarez
Keyword(s):  
Distributive Lattice ◽  
Partial Order ◽  
Directed Graph ◽  
Undirected Graph ◽  
Single Edge ◽  
Undirected Graphs ◽  
Modular Lattices

If (L, ≥) is a lattice or partial order we may think of its Hesse diagram as a directed graph, G, containing the single edge E(c, d) if and only if c covers d in (L, ≥). This graph we shall call the graph of (L, ≥). Strictly speaking it is the basis graph of (L, ≥) with the loops at each vertex removed; see (3, p. 170).We shall say that an undirected graph Gu can be realized as the graph of a (modular) (distributive) lattice if and only if there is some (modular) (distributive) lattice whose graph has Gu as its associated undirected graph.

Sign in / Sign up

Export Citation Format

Share Document