Questions tagged [breadth-first-search]
49 questions
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How to represent BFS and DFS between adjacency matrix and list?
I'm trying to figure out how to best represent BFS (Breadth First Search) and DFS (Depth First Search) on a graph, specifically between being represented as an adjacency matrix and an adjacency list. How do I determine which is a better…
MotherHorse
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Why do basic graph algorithms (BFS, DFS, Prim, Kruskal) have a similar structure?
This is my first post on CS Stack Exchange. For some time, I have been studying basic graph algorithms, mainly BFS, DFS, minimum spanning trees and their basic algorithms (Kruskal and Prim). One thing I have noticed, as I have used both Skiena's…
George1917
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Can Edge Belong to a cycle if it is part of multiple BFS products
Given a simple connected undirected graph. with V vertices and E edges.
Let e be some edge from E.
If I perform |V| different BFS runs - meaning started each time from a different vertex - and in every run e is part of the Spanning tree produced…
ohad edelstain
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The existence of a (nearly) quadratic time algorithm for 2-steps shortest path or smallest triangle
I am interested in two problems, which seem to be related, solving each will advance me in other possible directions.
In both problems, $G=(V,E)$ is a positively-weighted undirected graph. Denote its weight function by $w$.
Having $w$, a…
Mařík Savenko
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There exists some number $x$ so in any run of BFS from vertex $w$, so the distance from $u$ to $v$ in BFS tree is always $x$
Studying for my finals and stuck on the following question:
Prove or disprove: Given an undirected and connected graph $G=(V,E)$ and three different vertices $u,v,w\in V$ then there exists some number $x$ so in any run of BFS from vertex $w$, the…
vesii
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Comparing classical tree-search algorithms (BFS,DFS,A*,IDS) - when to use one or the other?
I have a question about classical tree-search algorithms as I will have an exam soon and this is the type of questions they might be asking. Although I know how to compare the complexities, optimality, and completeness, I would like to go a bit…
mariaprsk
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Find best path in an alternating graph
I am trying to solve the following problem: Given a directed graph, there is a robot in the start and it needs to reach the destination. Each movement takes 1 second, and every second the graph reverses each edges. The robot can stay at a node and…
Greggs
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DFS (Depth-first search) vs BFS (Breadth-first search) Space Optimizations
Problem
I am currently digging deep into some optimizations on the classical iterative approaches to both DFS and BFS algorithms. The material I'm currently using at my University presents both iterative approaches as follows.
Definitions:
G(V,E):…
Michel H
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An efficient way to find a pair of unrelated edges
I'm writing a program which uses an undirected graph to represent certain social connections, and I'm trying to check whether or not it's contains a specific induced subgraph.
Given a dense an undirected graph $G=(V,E)$ where I have a large amount…
Benicio Agüero
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2
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How to determine the time and memory complexity for solving a sliding-tile puzzle?
I have seen many posts which were related to algorithms for solving an N⨯N puzzle, but I could not figure out the time complexity or memory complexity in these algorithms, especially when we want to apply DFS and BFS for solving our puzzle.
For…
Aylin Naebzadeh
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The distinct-vertex $\alpha$-edge variant of the all-pairs shortest paths problem
The following problem is a variant of the all pairs shortest path problem: Given a weighted, directed graph $G=(V,E), |V| = n,|E| = m,$ and an integer $\alpha\ge 1$, how can I find an efficient algorithm to construct an $n\times n$ matrix where the…
Fred Jefferson
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Name of BFS variant with multiple queues with different priorities
Is there a name for the following variant of BFS that operates on trees with non-root starting point?:
Instead of a single queue that all neighbor nodes are added to when processing a node, two queues are used ($Q_A$ and $Q_B$).
Children nodes are…
JDN
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How to find more than 1 successive shortest paths between two vertices in unweighted and undirected graph using BFS?
I have tried to find and print more than one successive shortest paths between two vertices in the undirected graph. Using BFS as DFS will not be optimal in this case, as it can go deep into the stack.
Wrote this function but not getting the correct…
kamal
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"Visited" vs "Seen" Positions in Breadth-First Search
I'm struggling to understand why there is such a radical difference in the execution time and number of steps required by two seemingly similar algorithms for Breadth-First Search in a 2d grid.
In the Python program below, uncommenting the indicated…
Robin Andrews
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Why is the time complexity of bidirectional breadth first search still considered O(V + E)?
I understand that if the branching factor of the graph is b and distance of goal vertex from source is d, then the time complexity is O(b^d).
I also understand why that would be O(b^d/2) using bidirectional breadth first search.
What I don't…
Shisui
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