Related papers: Balanced Bidirectional Breadth-First Search on Sca…
Graphs and their traversal is becoming significant as it is applicable to various areas of mathematics, science and technology. Various problems in fields as varied as biochemistry (genomics), electrical engineering (communication…
Although Dijkstra's algorithm has near-optimal time complexity for the problem of finding a shortest path from a given vertex $s$ to a given vertex $t$, in practice other algorithms are often superior on huge graphs. A prominent example is…
We study {\em breadth-first search (BFS)} spanning trees, and address the problem of designing a sparse {\em fault-tolerant} BFS structure, or {\em FT-BFS } for short, resilient to the failure of up to two edges in the given undirected…
Graph searching is one of the simplest and most widely used tools in graph algorithms. Every graph search method is defined using some particular selection rule, and the analysis of the corresponding vertex orderings can aid greatly in…
The Breadth-First Search (BFS) algorithm is an important building block for graph analysis of large datasets. The BFS parallelisation has been shown to be challenging because of its inherent characteristics, including irregular memory…
The purpose of this report is to explain how the textbook breadth-first search algorithm (BFS) can be modified in order to also create a compact representation of all shortest paths connecting a single source node to all the nodes reachable…
It is well-known since the seventies of last century that Depth First Search (DFS) can be used to compute strongly connected components [RE. Tarjan. SIAM Journal on Computing, 1972] and Breadth First Search (BFS) can be used to compute…
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One…
Consider a search from the root of an ordered tree with $n$ edges to some target node at a fixed distance $\ell$ from that root. We compare the average time complexity of the breadth-first search (BFS) and depth-first search (DFS)…
We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially $n$ nodes and O(n) edges and monotone update sequences of either $\Theta(n)$ edge insertions…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
Breadth First Search (BFS) and other graph traversal techniques are widely used for measuring large unknown graphs, such as online social networks. It has been empirically observed that an incomplete BFS is biased toward high degree nodes.…
We provide the first approximation quality guarantees for the Cuthull-McKee heuristic for reordering symmetric matrices to have low bandwidth, and we provide an algorithm for reconstructing bounded-bandwidth graphs from distance oracles…
Search is a central problem in artificial intelligence, and breadth-first search (BFS) and depth-first search (DFS) are the two most fundamental ways to search. In this paper we derive estimates for average BFS and DFS runtime. The average…
Pathfinding makes up an important sub-component of a broad range of complex tasks in AI, such as robot path planning, transport routing, and game playing. While classical algorithms can efficiently compute shortest paths, neural networks…
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…
We propose a new exact method for shortest-path distance queries on large-scale networks. Our method precomputes distance labels for vertices by performing a breadth-first search from every vertex. Seemingly too obvious and too inefficient…
In the big data era, graph computing is widely used to exploit the hidden value in real-world graphs in various scenarios such as social networks, knowledge graphs, web searching, and recommendation systems. However, the random memory…
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.
Computing shortest path distances between nodes lies at the heart of many graph algorithms and applications. Traditional exact methods such as breadth-first-search (BFS) do not scale up to contemporary, rapidly evolving today's massive…