Questions tagged [dijkstras-algorithm]

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shortest path in color-weighted graphs

I want to find an algorithm to find the shortest path in a vertex-colored vertex-weighted graph. Every vertex with the same color has the same weight and the total weight of a path should be the sum ...
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2answers
108 views

Minimum distance in an undirected weighted graph to cover k nodes using teleportations

I have been practicing problems on graphs and shortest paths and I encountered a problem that I'm struggling to understand. Can you give me any tips and/or can you confirm that I got the general ...
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0answers
37 views

Solving shortest path problem with Dijkstra’s algorithm for n negative-weight edges and no negative-weight cycle

Although many texts state Dijkstra's algorithm does not work for negative-weight edges, the modification of Dijkstra's algorithm can. Here is the algorithm to solve a single negative-weight edge ...
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1answer
325 views

Why is DFS not suited for shortest path problem?

I am sorry for the repetition of the question. I understand that this question has already been answered before by the community, but most answers tend to focus on unweighted graphs. I want to know ...
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0answers
35 views

Fastest Algorithm for finding All Pairs Shortest Paths on Sparse Non-Negative Graph

As discussed here Johnson's Algorithm can be used to solve the APSP-Problem in $O(V^2\log V + VE)$ in stead of $O(V^3)$ for Floyd-Warshall. However, Johnsons Algorithm does quite a bit of work for the ...
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57 views

Find every path that passes through certain edges

I'm faced with the following problem: Given Directed and unweighted graph, where each edge E has two attributes Goal Find every path through the 3 (or more) given edges in a specific order ...
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0answers
13 views

Trivial clarification with the analysis of the Dijkstra Algorithm as dealt with in Keneth Rosen's “Discrete Mathematics and its Application”

I was going through the text, "Discrete Mathematics and its Application" by Kenneth Rosen where I came across the analysis of the Dijkstra Algorithm and felt that the values at some places ...
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0answers
34 views

Algorithm to calculate shortest path when updating the heaviest edge in a path [duplicate]

For a given graph $G=(V,E)$ and path $p= v_1 \to v_2 \to ...\to v_k$, $w^\ast(p)$ represents the weight of the path between $v_1$ and $v_k$ excluding max_edge. $$w^\ast(p) = \sum_{i=1}^{k-1} w(v_i, v_{...
2
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1answer
133 views

Modified shortest path problem

For a given graph $G=(V,E)$ and a given weight function $W$ lets say we define the new weight for path p to be the regular weight minus the heaviest edge in that path, i.e: $w^*(p)=\varSigma(w(v_i,v_{...
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2answers
165 views

Analysis of Dijkstra algorithm's (Lazy) running time

I'm trying to figure out the running time for a Dijkstra algorithm. All the sources I have read say that the running time is O(E * log (E)) for a lazy implementation. But when we do the math we get ...
4
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2answers
567 views

Find the shortest path that goes through an even number of red edges

I'm looking for an algorithm for the problem: "Given an undirected graph with positive weights on its edges and some of the edges are red and some are blue. Describe an algorithm that finds the ...
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1answer
140 views

Create an algorithm for computing the shortest path in O(m + nlogn)

So I'm trying to write an algorithm for computing the shortest path with constraints on the vertices you can visit in $O(m + n \log n)$ time. In this problem, we are given an indirect weighted (non ...
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1answer
163 views

find shortest paths from source to all vertices using Dijkstra’s Algorithm?

For Dijkstra’s,i can find shortest paths from source to all vertices in the given graph but how can i calling the algorithm |V| times taking each vertex as a source and store all tables ??? For ...
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0answers
25 views

Is It Of Much Practical Use To Actually Use Fibonacci Heap Over Min Heap In Dijkstra Algorithm?

I know that to get the best technical running time in Dijkstra's shortest path algorithms, using a Fibonacci Heap is the correct way to go. However, the internet and in CLRS state that Fibonacci Heap ...
2
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1answer
483 views

Gas Station Problem - Dijkstra's Algorithm variation

I am trying to find an algorithm which finds the least expensive route from one town to another. This is the general setup. There are a series of one-way roads from some towns to other towns. Not ...
2
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0answers
102 views

For which class of graphs can a minimum spanning tree always be associated to a shortest path tree?

Given a connected graph $G=(X,E)$ with positive edge weights. We assume that $G$ contains a unique min weight spanning tree $T_{\min}$ (this is true for example when for all the cuts, the edge with ...
3
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1answer
92 views

Dijkstra algorithm modification with exactly one relaxation on a directed graph where the weights of outgoing edges of a node are the same

Consider the standard version of Dijkstra's algorithm on directed graphs. Assume it is known that the input digraph $G = (V, E)$ has the following property: for all $v \in V$ the weight of all ...
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0answers
43 views

Is dijkstra's algorithm fastest possible algorithm for undirected graph with no additional data?

there are many similar questions, but I haven't found direct answer to this question. Consider I have undirected, weighted graph with positive weights, no additional data - hence no heuristic (so it ...
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0answers
10 views

Node ordering at contraction hierarchy of biDirectional Dijkstra

I try to understand the node ordering at contraction hierarchy. To me, ordering and contracting node looks impossible because when contracting a node, then it influence the other node. Therefore, it ...
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2answers
290 views

CLRS Exercise 24.3-4 - Confirm Output of a Program Claiming to Implement Dijkstra's Algorithm

I'm trying to better understand Question 24.3-4 From CLRS below: Professor Gaedel has written a program that he claims implements Dijkstra’s algorithm. The program produces $v.d$ and $v.\pi$ for ...
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2answers
94 views

“Subpaths” of Dijkstra's shortest path also shortest?

I have trouble putting this into formal mathematical terms, so let's suppose that I found the shortest path from A to E as A > C > D > B > F > E with Dijkstra's algorithm. Am I correct in assuming ...
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0answers
48 views

Routing algorithm for public transport without timetable

I'm trying to implement a simplified version of RAPTOR algorithm for journey planning. Raptor tries to find fastest route based on the arrival and departure time in each stop. There is a concept of a ...
0
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1answer
343 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 ...
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2answers
508 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 ...
3
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2answers
204 views

Why doesn't Dijkstra's use a shortest-path first search?

When using BFS search on an unweighted graph to find the single-source shortest paths, no relaxation step is required because a breadth-first search guarantees that when we first make it to a node, we ...
4
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1answer
406 views

Dijkstra without decrease key

I was reading through this paper, "Priority Queues and Dijkstra's Algorithm" by Mo Chen et al., which suggests using Dijkstra's without edge relaxation, but to rather to just insert new ...