Questions tagged [graph-traversal]
Questions about graph traversal algorithms such as BFS and DFS.
291
questions
0
votes
1answer
41 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
votes
1answer
30 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
vote
2answers
37 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 ...
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 ...
4
votes
2answers
126 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
vote
1answer
22 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?
0
votes
1answer
27 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 ...
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
44 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
62 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
35 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
18 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
2
votes
2answers
82 views
For what applications of the traveling salesman problem, does visiting each city at most once truely matter?
Traditionally, the traveling salesman problem has you visit a city at least once and at most once.
However, if you were an actual traveling salesman, you would want the least cost route to visit each ...
1
vote
2answers
58 views
Verifying connectivity of a graph in O(n^2)
I trying to solve the following problem in $O(n^2)$:
We have vertices which represents cities and a textfile containing an edge on each line. How many roads do we need to build to
make the graph ...
2
votes
0answers
42 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
48 views
is it always true that the depth of BFS is $\leq$ DFS?
I have a simple theoretical question in very basic algorithms, as the title mentions, is it always true that the depth of BFS is $\leq$ DFS?
From what I understand, the tricky part here is the ...
2
votes
1answer
55 views
How to merge a lot of trees into one single graph?
I have a few different trees, which resemble what the AST that compilers often deal with.
For example:
tree 1
( (a, b), (c, d) )
Imagine that each tree split represents the function "add", then ...
11
votes
4answers
3k views
Can the pre-order traversal of two different trees be the same even though they are different?
This question pretty much explains that they can, but does not show any examples of there being two different trees with the same pre-order traversal.
It is also mentioned that the in-order ...
2
votes
1answer
27 views
Minimize sequence storage by overlapping prefixes
I bumped into this problem today, and after a bit of pondering, I think I have a solution in $O(n^3)$, which is better than no solution or an $O(n!)$ solution, but my answer still isn't great. Can ...
3
votes
1answer
75 views
Cannibals missionaries problem - solving usings graphs
I am trying to solve the cannibals - missionaries problem; we have the number of cannibals, the number of missionaries and the position of the boat. We are trying to transfer all of them to the other ...
3
votes
2answers
67 views
Minimize number of DFS searches in a graph
I got a weird homework question about graph.
A helicopter is going to land on an island to check the n houses after an earthquake. Some of the two-way roads connecting the houses are destroyed ...
1
vote
0answers
93 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 ...
2
votes
1answer
103 views
Subtree with minimum sum of nodes' costs
Let's consider a tree with root $r$ ( not necessary binary) and to each node $i$ we associate a cost $\sigma(i)$ that can be negative, positive or zero. We want to select the set of nodes that ...
1
vote
1answer
82 views
Define the time complexity of Kruskal's algorithm as function
I am trying to define the time complexity of Kruskal's algorithm as function dependant on:
the number of vertices V
the number of edges ...
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
1answer
39 views
Is a subgraph of G always connected
I am trying to figure out if given a connect graph with N nodes and A edges, its subgraphs are connected.
In order word: given a graph G, can I have a subgraph of G that is not connected?
Or: can a ...
0
votes
1answer
38 views
Idea for a Graph Based Algorithm
Assume there is a Shopping Mall x and all the roads in the city are one way such that, irrespective of the path you take starting from x, you will always end up at vertex x. Device an algorithm to ...
3
votes
2answers
79 views
Fewest traversals to visit all vertices of DAG
I want to find the fewest traversals to visit all vertices of a DAG. To take a very simple case:
...
0
votes
0answers
49 views
Whats the time complexity of Prims Algo. without heaps (using priority queue)?
Here's my attempt:
Initialisation -
...
11
votes
3answers
1k views
What is the meaning of 'breadth' in breadth first search?
I was learning about breadth first search and a question came in my mind that why BFS is called so. In the book Introduction to Algorithms by CLRS, I read the following reason for this:
Breadth-...
2
votes
1answer
68 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 ...
0
votes
0answers
34 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, ...
1
vote
1answer
44 views
A problem to maximize the number of edges in a cycle while minimizing the total weight
I encountered the problem below and the only solution I came up with is branch and bound like that is used in TSP and I don’t think the bound I used is good enough. Are there any better idea on this?
...
0
votes
0answers
19 views
Find a path passing through the minimum number of odd nodes [duplicate]
Assume you have a undirected graph where each vertex is marked either odd or even. Given two even nodes, How do you find the path that passes through the minimum number of odd nodes in O(edges)?
Now ...
1
vote
0answers
67 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' ...
0
votes
1answer
17 views
Term for an A*-like pathfinding strategy where only the heuristic goal distance matters
I am trying to find a proper term for the A*-like best-first pathfinding strategy where the node to expand next is the one with the least estimated distance from the goal, regardless of its distance ...
0
votes
1answer
182 views
Finding topologically sorted connected components in directed acyclic graph
I am aware topological sort and connected component algorithms are very related, but I have been looking for an algorithm to simultaneously compute both, rather than one after the other, and I am ...
1
vote
1answer
37 views
Devising a way to spot a contradiction given a set of statements using graphs
If we had statements like: John is as tall as Mark, Mark is as tall as Sally, Chuck is as tall as Sally, Chuck is shorter than John.
Would there be a way to figure out that there is a contradiction ...
0
votes
2answers
161 views
Solving a in/equality constraint problem with graph search
You are given a list of m constraints over n distinct variables x1, ..., xn. Each constraint is of one of the following two types.
An equality constraint of the form xi = xj for some i!=j.
An ...
4
votes
2answers
112 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 ...
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 ...
13
votes
1answer
360 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 ...
1
vote
1answer
34 views
Shortest path in graph by flipping binary colored nodes to one color [closed]
Given a graph consists of two-colored nodes(e.g. white and black) and a starting node, and every time you visit a node, its color is switched(from black to white, or, white to black), how to find the ...
1
vote
1answer
46 views
How to perform local search to find maximal induced subgraphs?
I'm looking for efficient ways to perform local search to find maximal induced subgraphs that satisfy certain properties : a tree, a forest or a bipartite subgraph for example.
What I mean by local ...
1
vote
0answers
31 views
Order of Traversal in Bidirectional Dataflow Analysis
Does order of traversing CFG matter in solving bidirectional dataflow problems, from a performance perspective?
0
votes
2answers
70 views
Quick and space-efficient way to find whether two sets intersect
I hope you can help me -
Given a lot of sets containing integers,
I'd like for any two sets, to quickly (i.e. O(1)) ask whether they intersect.
Note that I don'...
3
votes
2answers
89 views
When searching graphs breadth-first and depth-first color the graph. Who un-colors the graph when the search is completed?
The depth-first and breadth-first algorithms for traversing graphs use a flag (or color) to mark nodes when they are visited. For example some forms of the algorithms use white/grey/black as colors. ...
3
votes
2answers
109 views
The complexity of the reachability-coreachability analysis of a finite state machine
Let $A = \{\Sigma,Q,\delta,q_{0}, Q_{m}\}$ be a finite state machine (FSM). A state $q \in Q$ is reachable if there exists a string $s \in \Sigma^{*}$ such that $\delta(q_{0},s) = q$. The state $q$ is ...
1
vote
2answers
130 views
“Process functions” in iterative and recursive depth-first search
I was reading The Algorithm Design Manual by Steven Skiena, and I noticed his use of "process functions" in depth-first search and breadth-first search. Consider the following pseudocode for depth-...
