Questions tagged [shortest-path]

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

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2
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1answer
177 views

Is there a way to reflect small edge-weight changes after computing Floyd-Warshall on a large graph?

I am working on a hex-based game in which I'm trying to pre-calculate pathfinding for a given map using the Floyd-Warshall algorithm. The map size is on the order of thousands of hexes (so maximum ...
2
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1answer
1k views

finding shortest negative cycle

Given a weighted digraph with positive and negative edge weights, what is the complexity of finding the shortest (uses the least number of edges) negative weight cycle in the graph? I know that I can ...
2
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1answer
422 views

When is the output of shortest path $\subset$ MST?

I was wondering if the output of an algorithm like Dijkstra was always contained in the minimal spanning tree, however, a counter example to this claim are cyclic graphs like: The shortest path $B \...
2
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1answer
1k views

How to find all shortest paths between two nodes in a weighted undirected graph? [closed]

How to find all shortest paths between node 1 and N in a weighted undirected graph? There can be multiple edges between two nodes. I want to find all nodes that can be on a shortest path. For example:...
2
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1answer
173 views

Do we want largest or smallest priority in the A* algorithm?

On this site http://algs4.cs.princeton.edu/25applications/ is described A* algothihm this way The A* algorithm is a problem-solving process where we put the start configuration on the priority ...
2
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2answers
2k views

Delivery Algorithm - Find shortest paths

Given - A center(lat=x,lng=y) 'C' from which a delivery boy makes a round trip. A delivery boy has a bag which may contain at the most 10 boxes to deliver. A set of points Di (lat=xi,lng=yi) ...
2
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1answer
3k views

Non intersecting paths in a graph

I'm trying to come up with a good algorithm for the following decision problem: Let $G=(V,A)$ be a directed graph and let $s,t \in V$. Are there at-least 2 non-intersecting paths from $s$ to $t$? By ...
2
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1answer
275 views

Can Floyd-Warshall be used to solve an APSP problem without copying the matrix?

According to CLRS, each iteration of the outermost loop (on $k$) makes a new copy of the adjacency matrix. Is it safe not to copy the matrix on every iteration? What I mean is, according to CLRS: $...
2
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2answers
1k views

Shortest path with odd weight

Let G be a directed graph with non-negative weights. We call a path between two vertices an "odd path" if its weight is odd. We are looking for an algorithm for finding the weight of the shortest odd ...
2
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1answer
25 views

Proving inequalities related to Dijkstra's algorithm

Define $spdist(s,t)$ as the distance of the shortest path from vertex $s$ to $t$. Define $IN(v)$ as the set of in-neighbors of $v$. Define $w(u,v)$ as the weight of the edge $(u,v)$. I am asked to ...
2
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1answer
122 views

Algorithm to find longest path in a tree that is smaller than x

Suppose we have a weighted binary tree $G$ where the nodes are towns and edges are streets with edge weights being the travel time and we want to find out whether it is possible to travel from any ...
2
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1answer
54 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 ...
2
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1answer
398 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 ...
2
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2answers
509 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 ...
2
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1answer
78 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 ...
2
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1answer
410 views

Understanding Bellman-Ford and Floyd-Warshall Algorithms as Dynamic Programming Algorithms

From my understanding, a problem amenable to a dynamic programming solution has these two properties: Overlapping Subproblems — The same subcase (a subsection of the overall problem) keeps ...
2
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2answers
457 views

Find the minimum path to every vertex using Bellman-Ford

I was studying the chapter 24 of the CLRS and got to the following question: 24.1-5 $\star$ Let $G=(V,E)$ be a weighted, directed graph with weight function $w : E \rightarrow \mathbb{R}$. Give an $...
2
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1answer
479 views

Applying Johnson's algorithm on undirected graph with negative edge weights

Currently we are discussing applying Johnson's algorithm on undirected graph with negative edge weights. And the graph may contains cycles, but the sum of weights of any cycle is guaranteed to be non-...
2
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1answer
845 views

Retrieve shortest path between two nodes using Bellman-Ford-Moore algorithm sequentially

This is my first question here and I hope you can help mt clarifying a doubt. Basically, I'm studying shortest path algorithms, for instance Dijkstra, Bellman-Ford-Moore, and I came up with a doubt. ...
2
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1answer
535 views

Perform Dijkstra on graph with negative edges by adding a big enough constant to every edges

I know that this doesn't work because shortest path with a lot of edges may have bigger weight than a longer path with less edges. But what if, you keep track of the edges that our current weight path ...
2
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1answer
85 views

Single-source shortest path algorithm for graphs representing stacked behavior

I am trying to compute a single-source shortest path in an interprocedural control flow graph (iCFG). That is a directed, unweighted, cyclic graph with edge labels. Some of these labels represent ...
2
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1answer
2k views

Shortest path from that passes through a set of edges once

Given a graph with weighted edges. How to find the shortest path from vertex $A$ to vertex $B$ that passes through a set of edges $X$ at most once? $X$ can be big. Slow solution: Finding shortest ...
2
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2answers
529 views

Shortest Path Passing All Routes

Is there a shortest path algorithim that calculates the shortest route passing all available roads, ending where you started? This differs from the Travelling salesman problem as you need to pass ...
2
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1answer
197 views

Connecting an unconnected forest of subtrees in a graph?

If I have a weighted graph $G=(V,E)$ and three subgraphs $T_1$, $T_2$ and $T_3$ in $G$ which are trees and all unconnected from each other. What is the best way to connect these three trees such that ...
2
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1answer
729 views

Shortest directed path connecting given subset of vertices

Given weighted directed graph $G = (V,E,w)$, where $w : E \to \mathbb R^+$ source vertex $v \in V$ vertex subset $U \subset V$ how to find a shortest directed path from $v$ containing all vertices ...
2
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1answer
95 views

Dijkstra without decrease key

I was reading though this paper, which suggests using dijkstra without edge relaxation, but to rather to just insert new nodes, cf page 16 for the pseudo code. But to me the code looks wrong. I think ...
2
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1answer
15 views

Performant algorithm to find edges without cross overs

I have a series of graphs with points plotted like this: Like in the image, I need to join these points to create a complete edge. I am currently doing this with nearest-neighbour, but because I don'...
2
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2answers
88 views

How can I avoid re-computation of Dijkstra algorithm if I add or remove one edge from a graph?

I have a nested graph filtration and each step I have to find the shortest path between two nodes. At each step I just add one edge to the graph so the re-computation of the Dijkstra algorithm is ...
2
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1answer
44 views

Thorup : What is the meaning of super distance?

While reading Thorup's Algorithm to solve SSSP problem, I have one point that I can't understand: super distance. It says: "For each vertex we have a super distance $D(v)\geq d(v)$" $d(v)$ must ...
2
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1answer
77 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 ...
2
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1answer
248 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
212 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,...
2
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1answer
56 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: ...
2
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1answer
62 views

Shortest path with nodes containing collectibles of negative cost

Suppose you have a graph with weighted edges and nodes. Edges always have non-negative costs (representing e.g. fuel costs), and nodes always have non-negative benefits (representing e.g. collectible ...
2
votes
1answer
65 views

How to find MST for each source

Let's say I have a map with factories and selling points. I want to trace the paths from factories to the selling points with the lower possible cost. The image bellow is an example of a possible ...
2
votes
1answer
44 views

Comparing nodes in A*

Nodes in the open list in A* will be sorted by their f-cost, but if the f-cost of two nodes are equal, will their h-costs instead be compared? I'm asking because I've seen implementations where the h-...
2
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1answer
128 views

LPA* implementation keeps looping

Short story I am currently trying to implement LPA* in an existing navigation system and find the algorithm seems to loop forever, expanding the same vertices over and over again. I am wondering what ...
2
votes
1answer
372 views

Conditional Shortest Path Through Weighted Cyclic Directed Graph

Vertices in my graph are composed of {name, category} where category is one of {red, grn, blu, ylw}. Edges in my graph are weighted and directed. In the visualization, the thick end of the edge ...
2
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1answer
90 views

Dijikstra implementation in books subtly different

I was reading about Dijkstra algorithm and was referring two books 1) Introduction to Algorithms by Cormen Section 24.3 2) Algorithm design by Kleignberg Section 4.4 And found a subtle difference in ...
2
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1answer
4k views

Single-Source Shortest Path with at most k edges using Dijkstra's algorithm

I am trying to solve a bounded SSSP problem as follows: Given a connected weighted graph with non-negative edges (might have cycles), find the shortest path from a vertex s to a vertex t with ...
2
votes
1answer
56 views

Why do admissible functions allow $A^*$ to retain correct shortest path computations?

I was reading about how to use $A^*$ and was told that: A heuristic is admissible if $h(u) \leq \delta(u,t)$, where $\delta(u,t)$ function indicates that the shortest path from $u$ to $t$. I was ...
2
votes
1answer
289 views

Variation on Bellman-Ford Algorithms?

We have a Directed Graph with 100 vertexes. v1 --> v2 --> ... v100 and all edges weights is equal to 1. we want to used bellman-ford for finding all shortest paths from v1 to other vertexes. this ...
2
votes
1answer
357 views

How does Hassin's algorithm for the Restricted Shortest Path work?

I'm studying the Approximation For Restricted Shortest Path Problem paper and don't understand what he is doing. In particular, I wonder why it is important that one computes upper and lower bounds $...
2
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1answer
88 views

Optimal path through a DAG with sparsely available edge weights [closed]

I would like to create a plot of certain metrics that are collected at revisions of a software system. The objective of the software engineers is to minimize those metrics. For version control, the ...
2
votes
1answer
238 views

Finding path with minimum weight

There is a river which can be considered as an infinitely long straight line with width W. There are A piles on the river, and B types of wooden disks are available. The location of the $i$-th pile ...
2
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0answers
18 views

Maintaining SCCs in directed graphs (on-line, under edge deletion) with ES-trees

I'm interested in efficiently maintaining the set of strongly connected components (SCC) in a directed (unweighted) graph under edge deletions only. While searching for ways I came across an article [...
2
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0answers
49 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
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0answers
33 views

Given complete graph, find optimal path with two costs on each edge

We are given complete graph, such that each edge has two costs $a \text{ and } b$. We should find path that passes through each node once and has minimum total cost. Cost of a path is the maximum of ...
2
votes
3answers
107 views

Shortest path between any origin to any destination through some way stations

How can one find the shortest path between any one of the origins to any one of the destinations through a number of way stations on the way using Dijkstra algorithm? You can visit those way stations ...
2
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0answers
143 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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