Questions tagged [graph-traversal]
Questions about graph traversal algorithms such as BFS and DFS.
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Bridges and Edge Disjoint Paths
So , Basically assume there is a graph $G$ which has no bridges. Is it always true that there exists two edge disjoint paths between any two vertices in the Graph ?
$\text{My Attempt at the Proof}$:-
...
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Why does this BFS solution work for this question about euclidean distance and what's its complexity?
Given a matrix of 1s and 0s where 0 represents houses and 1 represents stores, find the square of minimum Euclidean distance of every house to nearest store. Return it as a vector of vector.
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Please explain the algorithm for finding bridges in graph?
let, low[] and disc[] be two 1D arrays
disc[i] stores the discovery time of node[I]
low[i] stores the lowest value between disc[i] and discovery time of children of node[i]
I'm curious that what is ...
1
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1answer
14 views
Matching vertex values with sum of edge weights on bipartite graph
Earlier this week I asked this question (please review):
Imagine StackOverflow started offering a subscription where companies
could buy X number of impressions per month for a set of tags.
...
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0answers
15 views
Logspace reduction from PATH to 2SAT
It is known that PATH (given a directed graph G and two vertices s,t is there a path in G from s to t), and 2SAT are NL-complete problems. Find a logspace reduction from PATH to 2SAT.
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1answer
50 views
Efficiently finding “unfounded edges” in a strongly connected graph
While implementing a debugger I've encountered a problem I need to solve concerning dependency graphs. I've simplified it as follows:
Consider a strongly connected graph G = (V,E).
We define a ...
3
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2answers
39 views
Finding a hamiltonianISH path in a graph
Problem statement
Given a graph of all the blue squares in the following image where each blue square is connected to other blue squares in all 4 cardinal directions.
Given any starting node.
What ...
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2answers
80 views
Iterative Depth First Search for cycle detection on directed graphs
I found this pseudocode on Wikipedia, and looks very elegant and intuitive:
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0answers
32 views
small world networks properties
Small-world networks have two properties: clustering coefficient and average node-to-node distance
my questions are: 1- Can a disconnected graph ( which may include multiple connected graphs) hold a ...
2
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1answer
61 views
In a DAG, finding the path with the highest score
Given a directed, acyclic graph in which each node has an assigned integer score, what is a fast way of finding the path from a start and end vertex with the highest cumulative score? I thought of a ...
2
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1answer
34 views
Number of `m` length walks from a vertice with steps in [1, s]
The problem is stated as the following:
We are given a grid graph $G$ of $N \times N$, represented by a series of strings that describe vertices s.t.
$L$ is the vertice we're interested in
$P$ are ...
1
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1answer
63 views
Some paths in directed graph
Given directed graph $G = \langle V, E \rangle$, such that some vertices are red, and some vertices are black, and some edges are blue or green, decide for all vertices $v \in V$ if there is path from ...
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Graphs which favour BFS over DFS and vice versa
I am trying to figure out what kinds of graphs are better suited to BFS and which are better suited to DFS. However i'm struggling to visualise what kind of graphs favour which search. Could someone ...
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0answers
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Restoring the minimum vertex cover on bipartite graph from the maximum matching
I had to solve a problem on finding the minimum vertex cover on a bipartite graph, and I used the Kőnig's theorem and reduced it to maximum matching problem on bipartite graph, which is easily ...
3
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1answer
68 views
Existence of walk in undirected connected graph where nodes must end with assigned value
We have a graph with $N$ nodes and $N-1$ undirected edges, where it's possible to reach one node from any other node. Each node will get assigned a value randomly from [1,...,10]. We want the value of ...
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0answers
69 views
Shortest tour visiting given set of nodes in knight tour graph
Problem:
Given knight tour graph $G$ ($8 \times 8$ nodes) and a set of nodes $\{ v_{1}, v_{2}, \dots, v_{n} \} = V \subset V(G)$, find a minimal length tour in $G$ that visits all nodes from $V$ (...
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algorithm that finds minimal vertex cover of a given vertex
i am looking for a simple algorithm that gets as an input an undirected graph and a vertex in the graph and outputs the minimal vertex cover that v belongs to.
not sure on how to do it correctly, ...
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About shortest cycles in undirected graphs
In an undirected (and unweighted) graph, to find the shortest cycle containing a specific vertex $s$, it is usually said to run a BFS from $s$ and the first time to find a re-visit, then that is the ...
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Is it possible to implement iterative pre/in/post-order traversal with only one stack?
All iterative algorithms I've seen for pre-order, in-order, and post-order traversals of trees have used two stacks. Is it possible to do it with one? I've been thinking about it for ever, I haven't ...
1
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1answer
71 views
Determine whether there exists a path in a directed acyclic graph that reaches all nodes without revisiting a node
For this I came up with a DFS recursion.
Do DFS from any node and keep doing it until all nodes are Exhausted. I.E. pick the next unvisited node once you cannot keep recursing.
The element with ...
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0answers
32 views
Making graph acyclic by removing back edges in depth first and breadth traversal
I came across following points:
Removing all back edges produced by DFS makes the graph acyclic.
For a directed graph, the absence of back edges with respect to a BFS
tree implies that the ...
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0answers
15 views
Comparing shortest path distance and relation between two modes present in FIFO queue at the same time during breadth first traversal
I came across following problem:
Consider two vertices $a$ and $b$ that are simultaneously on the FIFO queue at same point during the execution of breadth first search from $s$ in an undirected ...
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1answer
64 views
Dijkstra's algorithm - Finding additional paths with same weight but different edges
given a network with n stations. assuming the shortest between s,t was found using dijkstra's algorithm. let that path be denoted as $(a_1,a_2,...,a_k)$
assume that between the nodes s and t, there's ...
3
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1answer
40 views
Algorithm for finding “mean center” of unweighted graph
I have a large sparse unweighted undirected graph (20M vertices, 60M edges) and would like to find what I'm calling the "mean center" (the vertex w/ shortest mean distance to all other vertices. Does ...
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2answers
118 views
Dijkstra and A* Algorithms: Why is A* faster?
I am learning about Dijkstra's Algorithm and the A* Algorithm and I have manually worked through the graph attached here, which is supposed (I think) to demonstrate that the A* Algorithm is faster ...
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23 views
Finding the minimal path from S to T that visit all vertices
So I have a complete and directed graph with weights.
I wish to find the shortest path from S to T that visits all other vertices in the graph at least once.
Another important piece of information I ...
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0answers
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How do programs like Apache Airflow/ Luigi determine shortest path and how does that relate to graph theory?
I am looking for a simple layman's term explanation on how do programs like Apache Airflow or Luigi (or any Task/ETL schedulers) determine the shortest path to complete a certain task and make it ...
0
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1answer
134 views
Why is my algorithm version so slow with this input?
Here I'm trying to do a comparison of two simple as possible algorithms, solving the symmetric travelling salesman problem, finding the optimal solution without the support of heuristics. I'm showing (...
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1answer
50 views
Breadth First Traversal for graph with multiple connected components
I read BFS and DFS from CLRS and realized that the BFS algorithm does not consider graph with multiple connected components but only with single connected component, whereas DFS algorithm considers ...
2
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1answer
276 views
O(V+E) algorithm for computing chromatic number X(g) of a graph instead of brute-force?
I came up with this O(V+E) algorithm for calculating the chromatic number X(g) of a graph g represented by an adjacency list:
Initialize an array of integers "colors" with V elements being 1
Using ...
4
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2answers
392 views
Find all nodes on simple paths between two nodes in cyclic directed graph
Given two nodes U and V in a cyclic directed graph, how can I find the set of nodes that are part of a simple path from ...
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0answers
27 views
Finding all non-comparable nodes in DAG
I have a DAG and I want to list all pairs of vertices that are not comparable (there is no path from the first to the second or the second to the first).
In this image (taken from this StackOverflow ...
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Find all Eulerian cycles in a directed graph
I am trying to create an algorithm that can find all Eulerian cycles in a directed graph. I was able to make an algorithm that can find one cycle in the graph, but I don't know how to find all the ...
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2answers
95 views
Graph theory: BFS (Breadth First Search) - why is current processed first?
I am referencing some code I found on GeeksForGeeks.com: Why is the current node printed (and processed) first before its children are processed? Wouldn't "breadth first" mean "Process children first, ...
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Is there a Weisfeiler-lehman kernel for directed, labelled and with cycles graphs?
I have a set of labelled, directed and cyclic graphs and a I need to perform a supervised learning algorithm in this data.
I have found a single paper A Persistent Weisfeiler-Lehman Procedure for ...
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Find the 'best' longest common subsequence
I am writing a program that computes and displays diffs. I implemented Meyers algorithm that computes the LCS between 2 subsequences (seq1 and ...
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1answer
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Is there an example of when DFS will not return the min. spanning tree?
If we have a connected, weighted, undirected graph. Can anyone provide an example where DFS will not return the MST? No matter what vertex we start from ?
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1answer
60 views
Computing a pre-topological sort using a BFS/a queue
Computing a topological sort in a DAG using a queue simply amounts to putting the nodes with indegree 0 in a queue, and going through the queue removing these nodes from the graph and adding the nodes ...
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BFS vs DFS, and Timing of Marking Vertex as Visited
The Wikipedia article on Depth-Frist Search states that:
The non-recursive implementation is similar to breadth-first search
but differs from it in two ways:
it uses a stack instead of a ...
2
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1answer
44 views
An algorithm for topological sorting based on depth-first search: why do we need two tags?
Wiki gives an alternative algorithm for topological sorting is based on depth-first search, as follows:
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2
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1answer
51 views
Arranging Colors in a Grid; Two Dimensional TSP?
I am working on an interesting problem, which I believe can be solved algorithmically. I have a 6x8 on which I am attempting to arrange 48 color swatches, such that the transition from each swatch to ...
2
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1answer
57 views
Efficiently compute the sum of edge weights product of all possible path in a DAG
I thought of using Depth First Search (DFS) to find all possible paths in O(|V|+|E|). However, computing the product of all the edge weights for a path is O(2^N). Is there any way to compute this more ...
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1answer
86 views
binomial tree number of nodes
Does anybody knows that how we can assign number to nodes for binomial tree . I mean how we can represent the number of nodes by array? please give me hint I am really confused .
2
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1answer
88 views
How to deal with parallel edges between two vertices in cycle detection using BFS in an undirected graph?
I am new to Programming and learning Algorithms and was studying BFS when I read that BFS could be used for cycle detection. I tried to implement the same on an undirected graph G with Adjacency List ...
1
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2answers
48 views
Find the minimal tank capacity to be able to travel from any city to any other
There are $n$ cities in the country. The car can go from any city $u$ to city $v$, On this road it spends $w_{u,v} > 0$ fuel. At the same $w_{u,v}$ can differ from $w_{v, u}$. The task is to find ...
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Detecting whether a node belong to a cutset with the least memory consumption as possible
I'm working on a problem about connected components implemented by cutsets.
Given a cutset, I want to determine whether some node lies within the connected component created by such cutset. The most ...
4
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2answers
271 views
How to evaluate all possible groups of adjacent tiles in 2D array?
I'm working on a tile based game idea in Javascript. It's a math puzzle game where players move around tiles with numbers on them, and the goal is to connect groups of tiles that have a sum of certain ...
1
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1answer
86 views
Directed graph reachability
Given a directed graph G(V,E) and a node s, how do we determine what nodes are reachable from s? Do I need simple traversal algorithms or do I need to look at Tarjan's algorithm?
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1answer
35 views
Strongly connected graph proof
Here I have a proof related to strongly connected graph from Algorithms book.
However, when I run DFS on the following 2 strongrly connected graph, I get different result than the proof.
According ...
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Why is BFS “vertex based” and DFS “edge based”?
I am trying to understand the various differences between Breadth-first and Depth-first search on graphs. Two sources state that BFS is "vertex based" and DFS is "edge based" even though in ...
