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Questions tagged [graph-traversal]

Questions about graph traversal algorithms such as BFS and DFS.

66 questions with no upvoted or accepted answers
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13
votes
1answer
361 views

Steps that guarantee exiting a maze

Given a 2-dimensional maze where you can give 4 commands "move up/down/right/left". Knowing the maze but not where the person is, how to find the minimum sequence of commands that guarantees exiting ...
7
votes
1answer
755 views

Find shortest paths in complement graph

I'm looking for an algorithm that receives as input a vertex $s$, and finds the shortest paths from $s$ to all vertices in the complement graph (undirected). The algorithm should run in $O(V+E)$ time, ...
5
votes
1answer
503 views

Shortest path in a known room for a Roomba

I had an interview question once which asked for an algorithm to ensure a Roomba vacuum cleaner visited/vacuumed every "cell" in an unknown shape/size room with unknown obstacles. Depth first search ...
4
votes
2answers
114 views

Find maximal subgraph containing only nodes of degree 2 and 3

I'm trying to implement a (Unweighted) Feedback Vertex Set approximation algorithm from the following paper: FVS-Approximation-Paper. One of the steps of the algorithm (described on page 4) is to ...
4
votes
1answer
3k views

When to use DFS and when use BFS?

Preparing for an interview. I see two cases where each one is specially suited BFS: When you need to find shortest path between vertices (if one exists). DFS: If you need to find cycles in a ...
3
votes
2answers
495 views

is it possible to determine using a single depth-first search, in O(V+E) time, whether a directed graph is singly connected?

I'm working on exercise 22.3-13 of CLRS (Intro to Algorithms 3rd edition): A directed graph $G = (V, E)$ is singly connected if the existence of a path from $u$ to $v$ implies that $G$ contains at ...
3
votes
0answers
68 views

Visiting all train stations

When I went to London, I wondered how to visit all the London Underground stations as fast as possible. Given a randomly-chosen start station, timetable of train arriving & departing of every ...
3
votes
0answers
760 views

Tree of Despair: Collecting Data from a Tree with Multiple Types of Branching

Provided is a tree with three types of node. The structure of the tree cannot be modified and traversal of the tree is limited to querying a node for its children or its parent. The objective of the ...
3
votes
0answers
57 views

Heuristics to Find Circuits Allowing for Vertex Revists

I'm currently working on a project discussing applications of the Delaunay Triangulation, and the primary use-case is applications to TSP (or relaxations of the problem). See: http://www.lancaster....
2
votes
0answers
43 views

Similar-path shortest paths

Consider a directed graph with an out-degree of 2 for every vertex, i.e. all vertices have exactly two outgoing edges. This means, considering $n$ as the number of vertices, that the number of edges ...
2
votes
1answer
70 views

Directed graph where DFS returns on a node before all its child nodes are visited?

Give an example of a directed graph in which a depth-first search backs up from a vertex $v$ before all the vertices that can be reached from $v$ via one or more edges are discovered. My professor ...
2
votes
0answers
317 views

How to traverse a graph in reverse dfs order

For kosaraju's algorithm to traverse the graph in reverse order the naive solution is to reconstruct the original input graph in reverse order and dfs on it. Is there any way I can avoid creating ...
2
votes
0answers
122 views

Algorithm to find nodes with given a distance

We have a map of a branching river without any islands (tree of confluences, see picture), there are piers on the river bank ( not necessarily on the confluences). We are given the distances between ...
2
votes
0answers
32 views

Inferences about Branching in TSP algorithm

I am building a program that uses branching-and-bounding to find an optimal path in a complete graph (the heuristic, faster algorithm is the second part). I have to begin and end at node 0. I was ...
2
votes
0answers
133 views

IDS algorithm optimality for grid?

My homework is implementing algorithms BFS, DFS, depth-limited and IDS for the map as a 2D grid with 8 directions of movement. I read that the IDS algorithm is optimal, but in my case is not optimal ...
1
vote
0answers
98 views

Maximum size of BFS open set on a grid

I have a 2D grid of infinite size that can either be 4-connected or 8-connected (as defined in https://en.wikipedia.org/wiki/Pixel_connectivity). I am implementing breadth-first search on this grid ...
1
vote
0answers
68 views

Algorithm for finding single input/output sub graphs

I'm running into an interesting directed acyclic graph (DAG) problem and was wondering if this is a known problem and if it has an efficient algorithm for it. I will use 'graph' and 'DAG' ...
1
vote
0answers
35 views

$n$ machines, $n$ types of jobs with $q_j$ jobs, minimizing the cost

I have this problem A firm has $q_j$ jobs of type $j$, where $1 \leq j \leq n$. It also has $[n] = {1,2,...n}$ machines. Machine $i$ can service any job of type $j$ where $j ≤ i$. The cost of ...
1
vote
0answers
32 views

Order of Traversal in Bidirectional Dataflow Analysis

Does order of traversing CFG matter in solving bidirectional dataflow problems, from a performance perspective?
1
vote
0answers
87 views

Enumerate all re-convergent paths in a digraph (with cycles)

I'm looking for an algorithm to count and enumerate (separately, if differing complexity) all the reconvergent pathsets in a simple, directed, non-weighted graph, which may contain cycles. That is, ...
1
vote
1answer
124 views

Post numbers in DFS tree of an undirected graph

How could you prove: An edge (u,v) is part of an undirected graph G. If post(u) $<$ post(v) (i.e. the post number of u is smaller than that of v) then it implies that v is an ancestor of u in the ...
1
vote
1answer
306 views

Find a path that contains specific nodes without back and forward edges

I have a directed graph and and a set of nodes(set = [1,2,5,9,24...]). I want to find a path that contains all the set of nodes and this path dont contain back edges(cycles) and forward edges. For ...
1
vote
0answers
53 views

Dynamic path planning and waypoint sorting

Good evening everyone, I have a question that I am having a bit of trouble formulating properly and thus it is making it complicated to look up literature on the subject. What I am looking for is a ...
1
vote
0answers
143 views

Efficient ways to avoid cycles in a graph

I am trying to implement an algorithm called the 'rapidly exploring random belief tree'. The aim of this algorithm is to come up with a path for a robot, which, instead of connecting start and goal ...
1
vote
0answers
136 views

How to systematically think about building implicit tree or a search space graph?

I often see DFS is used interchangeably with backtracking specially in many permutation, combinations and subset problems. But usually DFS has implicit tree and does backtracking at leaf nodes whereas ...
1
vote
0answers
303 views

Multithreaded algorithm to traverse DAG

I have a DAG of tasks designed as: DAG { Dictionary<NodeAddresses,Node> } Node { List<Node> Parents; List<Node> Children; Task T; } ...
1
vote
0answers
51 views

Pathfinding when the graph varies over time

Let's say I want to simulate a very large number of travelers booking flights. For example, a traveler might want to fly from New York to New Delhi. There's no direct flight from New York to New Delhi,...
1
vote
0answers
383 views

Dijkstras Algorithm with Bounded Integer Edge Weights

I don't really understand how we can use the fact that the edge weights are integers in the range [1, 2, ... , C] in order to speed up the computation of Dijkstra's algorithm. I read this lecture but ...
1
vote
0answers
58 views

Looking for name of siblings-first-depth-second traversal order

I've had to come up with a traversal order/algorithm for a project, and I am wondering if it has a name. The requirements of the algorithm are: it visits the parent before the children. it visits ...
1
vote
0answers
92 views

Node-weighted CSP in Prim's algorithm?

I'm looking for an algorithm which would find a minimal spanning tree given certain constraints (CSP) about importance of some nodes, e.g. consider a graph with next distance matrix: $$ \left[ \begin{...
0
votes
1answer
45 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 .
0
votes
0answers
18 views

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 ...
0
votes
0answers
18 views

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 ...
0
votes
0answers
46 views

Verifying the minimum cost from each node to a sink node in linear time

Problem Statement: Let $G= (V, E)$ be a directed graph with costs $c_e \in \mathbb{R}$ on each edge $e \in E$. There are no negative cycles in $G$. Suppose there is a sink node $t \in V$, and for ...
0
votes
1answer
73 views

how to prove correctness of this BFS algorithm?

Given an undirected connected graph, I wrote the following algorithm based on BFS. The algorithm detects wether this graph contains a cycle. If it contains a cycle then prints it. I'm pretty sure that ...
0
votes
0answers
18 views

Two algorithms for finding bridges in a graph that are almost the same

So I'm looking at an algorithm for finding bridges in an undirected graph. The thing is, there is a version of this algorithm that I've used so far that looks like this (C++) ...
0
votes
0answers
43 views

Maximum space consumption of stack and queue for DFS and BFS

I'm trying to determine the maximum memory consumption of the "pending nodes" data structure (stack/queue) for both travelings: BFS and (preorder) DFS. Since BFS and DFS while traveling graphs have ...
0
votes
0answers
19 views

What is the approximation for odd cycle transversal?

What is the best approximation for odd cycle transversal? (on general graphs) Sorry if this is easily found everything I found about odd cycles is about paramaterized complexity and kernels
0
votes
0answers
30 views

Are these algorithms for detecting cycles in directional graph correct?

I want to detect whether a subset of a directional graph reachable from a given root has a cycle, and print some useful debug information about the cycle. It's not a problem if there's a cycle not ...
0
votes
0answers
49 views
0
votes
0answers
35 views

Implementation of multiple sink shortest pair of disjoint paths problem for multigraphs

I would like to implement the shortest pairs of edge-disjoint paths of Suurballe and Tarjan for multigraphs in the interpretation of Banerjee et al. (http://web.cs.iastate.edu/~pavan/papers/short.pdf, ...
0
votes
0answers
289 views

A longest path can be found using DFS

The following is a Yes/No question. In an undirected unweighted graph $G$, a longest path between two given vertices $s$ and $t$ can be found using Depth-first search? If it is possible to use DFS ...
0
votes
0answers
80 views

How many roots are there in an undirected root

Given an undirected tree with 7 nodes how many roots would this tree have. My intuition tells me that because the tree is undirected it would either be 7 or 0. How would I solve this?
0
votes
0answers
17 views

Finding a path between 2 points passing through N points

Given a graph/plane with N points each at a given coordinate how could I find a path between 2 points via N other points where each point is weighted on how likely it is to be passed through. ...
0
votes
0answers
235 views

Longest-Path Layering algorithm

NOTES: there are a myriad of graph data structures, I use a spin-off of a directed adjacency hash. the code provide in this post is python3 on the premise that it ...
0
votes
0answers
40 views

The path with the highest sum of weights

Mr. Katsaros owns a rectangular olive grove divided into 5 rows and 4 columns. He notes down the amount of olives (pounds) possibly obtainable from each of 20 square sections. The picking starts from ...
0
votes
0answers
76 views

Multi agent graph traversal with edge discovery

Suppose we are given a set of agents (say $P_1 , \dotsc, P_M$), an undirected graph G(V,A) and a set of initial vertices on $G$ where each agent is located. Initially only the edges connected to these ...
0
votes
0answers
108 views

Time complexity proof of finding the $i$ object in binary search tree is $O(h+i)$ by inorder

I'm looking for time complexity proof of finding the $i$ object in binary search tree is $O(h+i)$ by inorder run. when $h$ is the height of the tree.
0
votes
1answer
234 views

How to deal with cost variation in a dynamic graph when applying Dijkstra

What are the methods to deal with variations in cost in a dynamic graph when applying Dijkstra? For instance, I select the shortest path in a graph, however, the weight of this path changed after I ...
0
votes
0answers
1k views

Shortest Path using DFS on weighted graphs

I read that shortest path using DFS is not possible on a weighted graph. I pretty much understood the reason of why we can't apply on DFS for shortest path using this example:- Here if we follow ...