# Questions tagged [graph-traversal]

Questions about graph traversal algorithms such as BFS and DFS.

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### How to remove 'skip' edges from a DAG? (How to find only the longest path from each node to each of its sinks?)

In two separate projects, I have come across this problem and I still don't have a good solution for it, so I thought it was worth describing here. Consider the following problem: I have a set of ...
19 views

### Graph traversal problem touching every node exactly once

Is there a name for the problem: Suppose you have a connected, undirected graph; find a path that touches every node exactly once. This is basically the complement of the Hamiltonian Path problem, ...
33 views

### Is longest-path with a specific source and destination impossible in polynomial time?

The problem of finding the longest path in a graph is known to be not be possible in polynomial time, that I am aware of. I am also aware that using DFS or BFS can give the shortest distance between a ...
36 views

### How to get the shortest simple path in a directed Graph with an additional constraint that it needs to use two arcs in the said path

I have a directed graph that has positive weights (but there are reverse arcs) and I am trying to find the shortest path between a given source, s and a given sink, ...
51 views

### Understanding depth-limited BFS time complexity

I'm trying to implement graph power calculation using BFS. According to Wikipedia, BFS with depth limit k will suffice (I'm using adjacency list representation, my graphs are sparse, so adjacency ...
155 views

### Updating a mst after increasing the weight of an edge in the mst

Suppose we have a weighted undirected graph $G$ and a minimum spanning tree $T$ Let $G2$ be a new graph by increasing the weight of one edge $e = (a,b)$ that is part of $T$. I'm using a common ...
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### Is there an algorithm for getting the boundary of a non-planar graph?

This is my first question here! If I have a non-planar graph where every vertex connects to 3 other vertices, and where the edges are allowed to intersect, how do I find the boundary of the graph? For ...
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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....
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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 ...
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### 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. ...
51 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 ...
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### 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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### 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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### 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 ...
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### 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 ...
36 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 ...
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### Determine if there is a path with alternating edge colours 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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### 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 ...
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### 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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### 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, ...
248 views

### 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 ...
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### 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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### 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 graph is ...
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### 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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### 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 ...
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### 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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### 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 ...