Questions tagged [shortest-path]

Questions about the algorithmic problems of finding shortest paths between nodes in a graph.

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Minimizing cost of shortest paths to a group of vertices by adding minimal edges to an unconnected vertex

Let $G=(V,E)$ be directed graph, where the weights of the edges are non-negative. The graph might have cycles, but without parallel edges. Consider a $T \subset V$, and $u \notin V$. I'm trying to ...
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280 views

How to handle negative edge weights in distance vector routing protocol with a digraph?

In a Distance Vector routing protocol each node implements a Bellman-Ford inspired algorithm that shares it's routing table (Distance Vector) with each of it's incoming links (upstream neighbors). ...
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25 views

Why does the inequality $d[v_i] \ge d[v_i−1] + w(v_i−1, v_i)$ hold when all vertices are labelled with their shortest path values upon?

Let $G = (V, E)$ be a weighted, directed graph with weight function $w : E \to R$, and let $s \in V$ be a source vertex. Assume that G does not contain a negative cycle reachable from $s$. Then, if we ...
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23 views

Shortest curve interpolating points with a constraint on the curvature

I'm looking for a method for determining a path for a UAV that interpolates a set of input locations, with a constraint on maximum curvature and given an initial velocity vector. The cost (length) of ...
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333 views

Analysing Dijkstra Algorithm by using different varieties of Data Structure

Question I want to analyse Dijkstra Algorithm by using different varieties of Data Structure. My solution Adjacency matrix to Store the Graph and Binary heap for Priority Queue. $...
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51 views

DAG Shortest Path — original citation for academic paper

I am writing to see if someone can point me to the original citation (assuming that a single work can be pointed to) for the single-source shortest path problem in directed-acyclic graphs (DAGs). ...
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455 views

Shortest path with minimal blue edges

Let $G=(V,E)$ be an undirected graph,such that ever $e\in E$ has a color-blue or red. Given $G$ and some $s,t\in V$ ,find an efficient algorithm that find from all pathes from $s$ to $t$,one with an ...
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54 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,...
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636 views

Edge weight changing during execution in shortest path algorithm

I have an undirected graph with weighted edges, in which I want to find the shortest paths from an initial node to every other node. Obviously Dijkstra's algorithm is usually a good choice, and I have ...
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178 views

State-of-the-Art techniques on dynamic shortest path computations

Suppose that I would like to find the shortest path between two vertices in a dynamic graph, where the cost function of an edge changes occasionally. I understand that an efficient algorithm to target ...
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1answer
597 views

Bellman-Ford: Find all nodes that have minus infinite distance to source

Given a weighted, directed graph (V, E) may contains some negative cycles and a source node s, I would like to know for all node ...
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17 views

Optimal linking in synchronous environment for shortest path tree problem

I am dealing with the Shortest path tree problem in the specific synchronous environment. In the following algorithm, initiator begin the execution calling primitives ...
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120 views

How do I apply a single iteration of Floyd's algorithm to an adjacency matrix? [closed]

I have the following adjacency matrix for a graph with nodes {a,b,c,d}: \begin{bmatrix} & & a& b& c& d\\ & & & & & \\ a& & 0& 1&...
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30 views

Finding next lightest path [duplicate]

Using Dijkstra algorithm, how can I find the next shortest path in a directed weighted graph? (When saying next, I mean that the next path must be heavier than the lightest path and not equal). The ...
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105 views

Fully dynamic k-shortest-path

I have a directed acyclic graph with positive edge weights. It is constantly changing in that nodes are deleted and added. For each change, I need to find the $k$ shortest paths. My current approach ...
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56 views

How to convert a search solution to a path to be tracked?

Let's say I have a space with obstacles and I'm trying to control a robot's movement while avoiding obstacles. I also have a start state and a goal state. I use a search algorithm to find the shortest ...
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1answer
778 views

find the shortest path between two nodes where the number of edges is minimal [closed]

Say you are given an undirected unweighted graph, where s and t are nodes from the graph. d(s,t) means the distance between s and t which outputs the number of edges. How do I find the the maximum ...
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361 views

Influence of edge number and priority-queue implementation on the runtime of Dijkstra

When we try to find the shortest path of a directed weighted graph using Dijkstra’s algorithm, is there a relation between the number of edges/vertices of the graph and the different implementations ...
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453 views

Parallel single source shortest path algorithm

Is there a deterministic parallel single-source shortest path algorithm (for graphs with non-negative edge-weights) that runs in sublinear time? The number of processors may depend on $n$ or $m$ (i.e.,...
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96 views

Shortest path with min-sum multiplication and Boltzmann distribution

My professor presented a method to find shortest paths using the min-sum multiplication and Boltzmann distribution. He multiplies the adjacency matrix many times and takes the $\beta$ of Boltzmann ...
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2answers
259 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
388 views

Find shortest path in undirected graph that goes through all vertices and returns to starting vertex

I have an undirected weighted graph like this one My task is to find the fastest path (with least weight) that goes from specified vertex goes through all vertices and returns to the starting vertex ...
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2answers
45 views

Is There Any Shortest Path Algorithm That Finds The Shortest Path Between Only Two Nodes

The Dikstra shortest path algorithm on a weighted graph, directional or bidirectional, pretty quick. There is also the Bellman Ford algorithm. However, these two find the shortest path between one ...
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2answers
506 views

Can Inverse of weights(1/weight,not negation) be used to find the longest path between two points by using dijkstra's algorithm?

Considering that there no cycles in the graph. I have seen the posts where the negation of the weights is suggested and to use Bellman-ford. But I was wondering if the inverse is possible.
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50 views

Online shortest path in ordered DAG

Suppose I have an edge-weighted connected rooted DAG $G = (V, E, r \in V, w \in E \to \mathbb{Z})$ where there exists a sequence of nonempty sets (called "levels") $L_0 = \{r\}, L_1 \subset ...
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2answers
622 views

When is bidirectional search unusable?

Is there any situation that bidirectional search on a graph is not applicable? for example is there any classes of graph that we can only use ordinary Dijkstra's algorithm, and can not use its ...
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1answer
31 views

What Is The Appropriate Action To Take When You're Shortest Path Algorithm Finds A Negative Weight Cycle?

Typing out negative weight cycle again and again is kind of annoying, so for the rest of the question I'm going to abbreviate it to NWC. I'm writing an optimized version of Bellman-Ford's Shortest ...
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1answer
39 views

Why does A* fail to find the fastest path when it reaches the goal?

I'm trying to understand how A* works on some simple examples, and something struck me as odd. I could fairly easily come up with situations in which A* "failed". Here is an example: Take a 2x2 grid, ...
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3answers
1k views

Modification of Dijkstra's algorithm

How to modify Dijkstra's algorithm, for wheel chair users, to take into account the road quality? There are three levels of quality: $1$ for pure concrete, $2$ for partly concrete and $3$ for rough ...
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2answers
619 views

Existence of shortest path in a graph with no negative cycles?

Suppose that the input graph $G$ does not have any negative cycles but however it is permitted to contain edges having negative weight. Let $s$ be the source vertex. How do I prove that for every ...
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2answers
774 views

Bellman–Ford negative path meaning

In the Bellman–Ford algorithm, what is the practical meaning of having a negative path between routers? I have tried searching the net but didn't find any data thanks Eli
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2answers
4k views

How to construct the found path in bidirectional search

I am trying to implement bidirectional search in a graph. I am using two breadth first searches from the start node and the goal node. The states that have been checked are stored in two hash tables (...
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1answer
98 views

Negative cycle detection using Bellman-Ford and its correctness

I recently started studying algorithms on my own using Cormen and MIT algo videos in YouTube. I am going thru Bellman-Ford. I have 2 doubts about the correctness of the algorithm: Why are we ...
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2answers
1k 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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2answers
424 views

Shortest distance from multiple points to one point

I am looking for an algorithm to find the shortest distance from multiple nodes to one end node. For example let $v_1,v_2,\dots,v_r$ be the nodes on a graph with distance $d_1,d_2,\dots,d_r$ to the ...
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1answer
744 views

Why does Dijkstra's algorithm not account for updating node distances after expanding a node?

Why does Dijkstra's algorithm not re-evaluate/re-expand nodes who have been expanded and later had their weight changed? For example, in the accepted answer of this question (link), if the algorithm ...
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1answer
2k views

Normalizing edge weights and the effect on Dijkstra's algorithm [duplicate]

If I had a graph $G$ with some negative edge weights, clearly Dijkstra's algorithm does not definitely halt, since it might get caught in a negative cycle (shedding infinite weight). However, would ...
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1answer
3k views

How to optimize Dijkstra's algorithm for a grid graph?

I'm trying to apply Dijkstra's algorithm to the Problem 83 on projecteuler.net. The problem reads: In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by ...
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1answer
134 views

How to prove that Bellman-Ford algorithm detects a negative cycle?

I have read that if we run the outer-loop of the Bellman-Ford algorithm for |V| times (where |V| is the number of nodes in the graph) and check if any distance has changed in the |V|th iteration (i.e. ...
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1answer
49 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
864 views

Does Floyd–Warshall work on all graphs?

Floyd–Warshall calculates minimum distance between any two vertices in the graph. ...
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4answers
3k views

Questions on shortest path and minimum spanning tree

T/F Questions Adding a constant to every edge weight does not change the solution to the single-source shortest-paths problem. Solution - False I think this should be True, as Dijkstra's Algorithm ...
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1answer
148 views

Is this a correct description of Dijkstra's algorithm

I am on a journey understanding Dijkstra's algorithm. My familiarity with mathematical terms is not great, so I have put the algorithm into my own English. I understand this is not ideal, but this is ...
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1answer
35 views

What am I missing in this application of Dijkstra?

When running Dijkstra against the following graph: 1 3 A -- B -- C \ / 2 \ / 1 \ / D ...I come up with the following: ...
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1answer
97 views

Is it possible that the diameter of a graph be shorter than the longest shortest path?

I used networkx to find the diameter of a graph that I have. It gave a diameter of 4. However, I found that between two particular nodes, using networkx's shortest path function, the path length is 5. ...
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1answer
135 views

Combining Runtime Complexity Expressions with respect to Dijkstra

If I have an algorithm that fills out an $|V| \times |V|$ table with for loops and an $O(1)$ sub-problem after running Dijkstra twice (outside the loop), I think I get the following runtime complexity ...
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1answer
3k views

Shortest path algorithm using Dijkstra with Fibonacci heap

Given an undirected connected graph $G=(V,E)$ with positive weights, where $|V|>2009$, and each vertex is of degree of at most $10$. Give an efficient algorithm to find the $2009$ closest nodes to ...
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1answer
5k views

Complexity of the Dijkstra algorithm

I'm little confused by computing a time complexity for Dijkstra algorithm. It is said that the complexity is in $O(|V|^2)$ - Wikipedia - Dijkstra, which I ...
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1answer
881 views

Shortest path in a matrix

I am trying to solve this problem, and i have tried multiple methods, but i must be missing something, here is the problem: Given a matrix MxN. Find the shortest path from (1,1) to (M,N), where each ...
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1answer
1k views

Betweenness centrality measurement ignoring inverse paths?

I'm implementing the Betweenness Centrality algorithm proposed by Brandes (first algorithm on this paper - also below), and I'm running into a very weird issue: it seems to be ignoring some paths (i.e....