Questions tagged [shortest-path]
Questions about the algorithmic problems of finding shortest paths between nodes in a graph.
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0answers
26 views
Shortest path with a given condition
The problem says to find the shortest way (the smallest amount of intermediary points), with given source and destination points, such that between two consecutive intermediary points there are two ...
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1answer
37 views
Minimum distance of nodes from a set of two nodes
In an unweighted tree, suppose that we want to delete (or mark) any node which is closer to node $v$ than node $w$ ($dist(x,v) < dist(x,w)$). The solution that comes to my mind is running two BFS, ...
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0answers
22 views
Bellman-Ford algorithm with n-1 iterations
I am supposed to find the graph for Bellman-Ford algorithm, where I have to use all $n-1$ number of iterations.
Can I use this graph, where S is my initial node?
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0answers
18 views
Reconstruct shortest path from a list of predecessors
I am trying to do a shortest path reconstruction with the given parameters:
an array P, which contains the predecessors of every vertex on a shortest path from S to I
a starting vertex S, defined by ...
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1answer
20 views
Using the decision problem, PATH in order to solve the optimization problem, SHORTEST-PATH in polynomial time
So, if I were using a black-box decision algorithm, PATH in which I could say, "does a path of weight k exist in this graph from ...
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1answer
53 views
Shortest Path in Layerwise Complete Graph
Consider a directed $k$ partite graph $G$ with a source node $s$ and a sink node $t$. Each vertex in the graph is labeled with a positive integer value. Both the source and sink are labeled with $0$. ...
2
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1answer
41 views
Bellman-Ford - is number of interations greater than diameter?
Diameter of a connected, undirected graph is the smallest natural
number d, so that between any two vertices of the graph exist path
of length at most d.
Prove or disprove: in Bellman-Ford is ...
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1answer
40 views
Is the number of shortest paths between every two vertices at most 4*n^3?
In every weighted graph with $n$-vertices
with negative weights,
with $n > 10$,
a weight can't appear $n$-times in graph,
there are between every two vertices at most $4n^3$ shortest paths.
I'm ...
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0answers
21 views
Finding negative cycle using Bellman Ford
Given a graph with |V| vertexes and |E| edges, I have to find a negative cycle, if there is one, in a graph.
The wanted complexity is O(|V|*|E|).
I was thinking about using Bellman-Ford to solve the ...
2
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1answer
40 views
Single-source shortest paths with even weight
I need help to find an algorithm that calculates the single-source shortest paths in a graph, with an extra condition that the weight of the path has to be even.
In another words, we have to find the ...
2
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1answer
38 views
shortest path tree algorithm
Suppose we are given a directed weighted graph $G=(V,E)$, a source vertex $s$ and the value of the cheapest path $\delta(s,v)$ for every $v \in V$.
I want to find an algorithm for the shortest path ...
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0answers
35 views
Advice on developing a “word ladder” finding program
I am a college student studying Computer Science. For the final programming assignment of the course I'm enrolled in I have to make a java program that can find the shortest possible word ladder ...
4
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1answer
98 views
Path between two vertices in directed graph without cyclic vertices
I have been searching online for some time but I have not found an answer.
Is there a polynomial time algorithm to find a path in directed graph between two vertices so that within the path no cyclic ...
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2answers
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-...
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0answers
15 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, ...
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1answer
88 views
Djikstra's algorithm to compute shortest paths using at least k edges
I have a graph G = (V, E) where each edge is bidirectional with positive weight. I want to find the shortest path from vertex s ...
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1answer
61 views
Multiple Source Shortest Paths in a weighted graph
In an unweighted graph, we can find Multiple Source Shortest Paths using the Breadth-First Search algorithm by setting the distance of all starting vertices to zero and pushing them into the queue at ...
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1answer
49 views
Minimal paths as solution of a linear program of a special network flow
Let $G= (V,E)$ be a given directed weighted graph, and $s,t$ two specified nodes, so that there is no negative cycle reachable from $s$, and $t$ is reachable from $s$.
We're looking for the shortest ...
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0answers
86 views
How can an A* algorithm visit all nodes?
Is it possible to find the shortest path and visit all the nodes in a graph by A* algorithm? If yes, how?
2
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1answer
101 views
Given directed connected weighted graph, check if d(v) = delta(s,v)
I'm having some hard time with this problem.
Can someone give me some clue/guidance?
This is an homework question, so please don't just solve it.
Given a weighted directed connected graph $G = (V,...
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1answer
114 views
Dijkstra’s versus Lowest-cost-first (best first), resolving some contradictions regarding complexity analysis
Our professor took three statements from various textbooks that seem to be a little contradictory regarding the complexity analysis of Dijkstra’s algorithm as well as the lowest-cost-first or best ...
4
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0answers
81 views
Can the running time be reduced to something lower than $O(d^4)$?
Imagine I have a weighted complete directed graph $G$ with $d$ vertices(so $d(d-1)$ edges) and I want to do the following:
Set $D$ to be a DAG with the same set of vertices but without any edges
sort ...
0
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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 ...
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1answer
39 views
Hitting probability of random walk within given number of steps
Given m,n dimensions of a 2D matrix; (i,j) initial co-ordinates; (x,y) final co-ordinates.
What is the probability of being at (x,y) after at most k steps if we start from (i,j) initially?
We can ...
1
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1answer
124 views
Floyd–Warshall algorithm on an undirected graph contains negative weight edges
According to this answer, the Bellman-Ford algorithm doesn't work when an undirected graph contains negative weight edges since any edge with negative weight forms a negative cycle, and the distances ...
6
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1answer
119 views
Finding a negative cycle in a bipartite graph
The Bellman-Ford algorithm can be used to find a negative cycle in a general graph, in time $O(|V||E|)$. Is there a faster algorithm for finding a negative cycle in a bipartite directed graph, where ...
0
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1answer
52 views
Distance function such that we visit every “color region” once [closed]
Consider the following image:
Starting at (0,0) top left, the objective is to find a dijikistra path to the bottom right.
We must go through each color exactly once, and once we go outside a color, ...
3
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1answer
103 views
Constructing a minimum spanning tree from an all-shortest path graph?
Given an $n \times n$ shortest path distance matrix $D$. And a complete graph $G(D)$ on $n$ nodes, where edge $(i, j)$ has weight $D_{ij}$. Furthermore, the distance matrix $D$ is computed for a ...
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1answer
56 views
Combinatorial Optimization: Shortest distance given sets of drivers and riders
Problem:
I have 2 sets, one of drivers and one of riders. All my participants need to reach one common destination. I wish to calculate the shortest combined distance in order for all participant to ...
2
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2answers
86 views
Given all pairs shortest paths matrix, find graph with minimum total sum of edges
I was looking at some problems about graphs, and I got stuck on this one. Namely, we have given matrix of size $N \cdot N$ representing the length of the shortest path in undirected graph between some ...
3
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2answers
139 views
How many iterations does the Bellman-Ford algorithm need for directed and undirected graphs
The Bellman-Ford algorithm on a graph with $n$ vertices, normally includes a loop executed $n-1$ times. Each time through the loop we iterate over the list of edges $(u,v)$ and relax $v$. Note that ...
2
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1answer
42 views
All pair shortest path in a tripartite graph
I have a tri-partite graph with three sets of vertices source, bridge and destination nodes. I want to find the shortest path between every vertex in the source set to every vertex in the destination ...
3
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1answer
27 views
Longest simple walk below a certain weight
Given a directed graph G and a starting vertex $v$ and a cutoff weight $w$, I want to find a simple walk with net weight < $w$ that visits as many nodes as possible. Currently, I have a recursive ...
0
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1answer
45 views
Running Dijkstra on particular graph with negative weight
After running Dijkstra on this graph from S, which shortest paths will be incorrect?
This graph has a negative weight, so which shortest paths will be incorrect? after my first attempt I got that Y ...
0
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1answer
107 views
Dijkstra complexity analysis using adjacency list and priority queue?
I just got to look at the Implementation of Dijkstra using adjacency list and priority queue. The time complexity is $O(E\log V +V)$, I tried looking for the proof but couldn't find one. Any help will ...
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0answers
33 views
Contraction Hierarchies minimal distance proof
I am trying to implement "Contraction Hierarchies" algorithm and reading the white paper and watching video lectures [6,7]. But still I can't understand proof for the following lemma:
Lemma 1. $d(s,...
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1answer
79 views
Shortest path from source to all vertices, but with some wildcards
Here is problem in Sprinklr Interview Experience | Set 5 (On campus – FTE for Product Engineer).
You are given a graph of $n$ nodes with $m$ bidirectional edges. Each edge has some value associated ...
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0answers
83 views
Successive shortest path without reduced costs
The successive shortest path algorithm, used to solve the minimum-cost flow problem, can be described as follows :
Successive shortest path (for minimum-cost flow) :
while all flow is not ...
2
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1answer
49 views
Djikstra algorithm analysis
My textbook says that the Dijkstra algorithm's runtime is $O(n) + O(m \log(n)) = O((n+m) \log(n))$. How did they come up with that?
Dijkstra algorithm pseudocode:
...
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1answer
26 views
How is Johnson's shortest path weighting function $\hat{w}(u, v) = w(u, v) + h(u) - h(v)$ proven by the triangular inequility?
Recap to the Johnson's shortest path algorithm:
By the procedure extending the original graph $G^\prime = (V^\prime, E^\prime), V^\prime = V\ \cup \{s\}, E^\prime = E\ \cup \{(s, v)\ |\ \forall v \in ...
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2answers
219 views
Understanding connection between minimum spanning tree, shortest path, breadth first and depth first traversal
In CLRS, in the later part of breadth first search topic, for unweighted graphs, it says:
At the beginning of this section, we claimed that breadth-first search finds the distance to each reachable ...
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0answers
50 views
Finding all edges on any shortest path between two nodes using dijkstra
Given a directed weighted graph, we need to mark all edges (represented by an ordered triple of (source,destination,weight) ) which lie on some shortest path from source to destination (there could be ...
3
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1answer
69 views
Intersection of two shortest paths in connected weighted graph
Let $G=(V,E)$ be a connected directed weighted graph with non-negative weights
on edges. Let $u,v,s,t$ be vertices in the graph $G$. I need to find an algorithm which in $O(|E|\log |V|)$ time checks ...
2
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0answers
101 views
Why is it true that given a monotonic heuristic function, A* can be seen as Dijkstra's algorithm where no node needs to be processed more than once?
Maybe I am missing something very easy and obvious.
But, I don't understand why estimate cost of source vertex is subtracted from the overall estimate cost, if heuristic function $h$ is monotonic: $$...
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1answer
32 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 ...
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2answers
271 views
Time complexity of Dijkstra's algorithm for sparse graph
I'm not sure I understand the answer to this question:
Question 9.
What is the running time of Dijkstra's algorithm in a graph that is sufficently sparse - in particular, $E=o(V^2/\log V)$, ...
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1answer
64 views
Computer Networks, OSI model
What layer of OSI model does define the route of information transmission between sender and receiver computers?
A) Session layer
B) Physical layer
C) Data link layer
D) Network layer
E) Transport ...
2
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1answer
121 views
Confused about the correctness proof of Dijkstra's algorithm
In the proof of the correctness of Dijkstra algorithm, there is a lemma stating as follow:
Let u be v's predecessor on a shortest path P:s->...->u->v from s to
v. Then, If d(u) = δ(s,u) and edge (...
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1answer
37 views
What's the usage of $S$ in Dijkstra shortest path algorithm in the book Introduction to Algorithms?
I don't understand how the $S$ is needed in dijkstra shortest path algorithm. For each node $v$ in $G.V$, the $v.\pi = previous\_node$ is used to denote it previous node in the shortest path to the ...
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1answer
37 views
Will MST find the shortest path for each pair $(r,v)$?
Will local best choice will lead to global best choice? In other words, I'm thinking about whether it's possible that the MST has to put its branch location in the middle of two far nodes ...
