Questions tagged [shortest-path]

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

115 questions with no upvoted or accepted answers
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12
votes
0answers
548 views

Optimal meeting point in directed graph

Let $G(V, E)$ be a edge-weighted directed connected graph and $v_1, \dots, v_n \in V$ be some vertices. Let $d(a, b)$ denote the length of the shortest path from $a$ to $b$, for $a,b \in V$. I need ...
11
votes
0answers
273 views

Change in the distances in a graph after removal of a node

Given an undirected unweighted graph $G=(V,E)$ and a node $s \in V$, we are looking for a vector $\operatorname{diff}[]$, such that, $$\operatorname{diff}[v] = \sum_{u \in V \setminus \{v\}}{(d^{G \...
7
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0answers
187 views

Algorithms for curve construction

I am interested in algorithms that construct continuous curves between two points in such a way that minimizes an energy functional of the curve. What sort of algorithms are most used for such tasks? ...
6
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0answers
1k views

Suurballe's Algorithm: Proof of Correctness

I was reading about Suurballe's algorithm on Wikipedia, for the shortest edge-disjoint paths problem, i.e. given nodes $s$ and $t$ finding a pair of paths between these nodes, whose accumulated weight ...
6
votes
0answers
332 views

Are there Some Pairs Shortest Paths Algorithms?

I know that there are All Pairs Shortest Paths algorithms. But I am not sure if they are effective if I am trying to solve the Pairs-Shortest-Path problem for a subset of my vertexes. The properties ...
6
votes
0answers
1k views

Stopping condition for goal-directed bidirectional search for shortest path

So I have a graph and need to find shortest path between two points in it. I need1 to do it it using bidirectional search. The bidirectional search should be goal-directed, i.e. A*. So let $l(u,v)$ ...
6
votes
1answer
435 views

Finding Shortest Paths of weighted graph using stacks

I will be given some kind of this graph as in the picture below. I've searched some algorithms but it seams as if it is something impossible for me to figure them out. In fact using Floyd–Warshall ...
5
votes
0answers
84 views

Find a minimum-cost pair of arc-disjoint paths, both within a given restricted distance

Is there a polynomial algorithm that can find a pair of arc-disjoint paths in a directed graph that has a minimum total cost, subject to the condition that both paths are within the same distance. ...
5
votes
1answer
568 views

Shortest path in a known room for a Roomba

I had an interview question once which asked for an algorithm to ensure a Roomba vacuum cleaner visited/vacuumed every "cell" in an unknown shape/size room with unknown obstacles. Depth first search ...
4
votes
0answers
84 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 ...
4
votes
0answers
738 views

A good heuristic for 2D Rubik's cube

I am looking for a good heuristic function for solving a 2D $n\times n$ Rubik's cube using A* search. There is a game already in the play store. The rules of the game: Swiping LEFT means the ...
4
votes
0answers
152 views

MST that contains a shortest $s,t$-path

Consider the problem in which we have an (undirected) graph $G=(V,E)$, weight function $w:E\to\mathbb N$ and a pair of vertices $s,t\in V$, and are required to determine whether there exists an MST $T$...
4
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0answers
133 views

Successive Shortest Paths vs Ford–Fulkerson

Can someone explain how exactly Successive Shortest Paths (SSP) is a generalization of the Ford–Fulkerson algorithm? I've found this stated in a few papers and websites as well as the Wikipedia page ...
4
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0answers
3k views

Fastest algorithm for shortest path with atmost k edges on a DAG with non-negative edge weights?

(Please note, this is not a duplicate to Shortest path with exactly $k$ edges OR Shortest path with a fixed number of edges. What I want is a better algorithm) The problem under consideration is to ...
4
votes
0answers
680 views

What is the complexity of Hoffman and Pavley's Nth best path algorithm?

I am currently working on a project where I'm using an implementation of Hoffman and Pavley's "Method for the Solution of the Nth Best Path Problem" to find n-th best path through a directed graph. ...
3
votes
0answers
86 views

How to extend Bellman-Ford to solve the $k$ shortest path routing?

Browsing the wikipedia I got to this page where it is said: Finding k shortest paths is possible by extending Dijkstra algorithm or Bellman-Ford algorithm and extend them to find more than one ...
3
votes
0answers
64 views

Dynamic all pairs shortest path edge removal

I have a planar(|E|=O(V)) undirected graph with positive edge weights. I have already calculated all pairs shortest path with Floyd–Warshall algorithm. Now I want to recalculate APSP with an edge ...
3
votes
0answers
142 views

How to minimize the sum of edge weight in the graph while keep the all-pair shortest path greater than a constant?

For example, if we have a graph G = (V, E) and a subset of vertices $U \subset V$. We can set $w(e)$ where $e \in E$ to be a non-negative real number. We want to minimize the total edge weight, but ...
3
votes
0answers
41 views

Defining preferred paths makes $A^*$ heuristic lose admissibility

In a geographical graph, where each edge's cost is equal to the physical distance between its nodes, one can be tempted to manipulate the cost of some of the edges, to make it a bit lower, in order to ...
3
votes
0answers
420 views

Algorithm to traverse all unblocked $1*1$ squares in a $n*m$ grid

Given a $n*m$ grid, some $1*1$ squares are blocked(can't be entered) and some are unblocked(can be entered). What is the algorithm which prints the shortest path, such that the path covers all ...
3
votes
0answers
86 views

Shortest paths in isomorphic graphs with different edge weights

I'm looking for a way to find the shortest paths from a source to all destinations in isomorphic undirected graphs with different edge weights. The only thing I can think of is using Dijkstra on each ...
3
votes
0answers
414 views

Assigning edge weights under shortest path constraints

We are given a graph $G = (V,E)$ and we need to find an assignment of non-negative edge weights (You must give every edge a non-negative weight). We are also given a set $R\subseteq V$ and mapping $c_{...
3
votes
0answers
326 views

Finding partial traveling salesman path of specified length

For a given set of nodes, I can find optimal paths that visit all nodes using various traveling salesman algorithms. As a subset of this problem, I would like to be able to find shortest partial ...
3
votes
0answers
930 views

Any algorithm for finding Euclidean shortest path with specific constraints in 2D?

I have the following problem: In a 2D space with polygonal obstacles, find the shortest path between two given point. Without additional constraints, we can reduce it to a graph problem by ...
3
votes
1answer
337 views

kth nearest vertex in a unweighted graph

Given an unweighted undirected graph $G$ with $10^5$ vertices and a subset $S$ of special vertices and an integer $k$, I want to find the $k$th nearest special vertex for each vertex. What algorithm ...
2
votes
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
votes
0answers
57 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
0answers
35 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
0answers
148 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: $$...
2
votes
0answers
128 views

Shortest route through ordered points

My algorithm-fu is really weak and I do not know how to express following problem in terms of any other problem known to me: Given a small rectilinear grid and coordinates of four cells in this grid (...
2
votes
0answers
60 views

IP algorithm for finding path in graph

Suppose for each positive integer $N$, we have a graph $G_N$ with $N$ vertices labelled $1$ to $N$ (so $\log N$ bits are required to specify a vertex). Suppose we have a PSPACE algorithm to determine ...
2
votes
0answers
40 views

Generating flight path for aerial photography

I need to generate the shortest possible path for aerial photography using a fixed wing unmanned air vehicle (UAV). The image below shows the area I'm going to search. The white cells are the cells I ...
2
votes
0answers
380 views

Algorithm - True shortest path for triangulated 3d-surface

I need to find true shortest path between two points. true means that shortest path can be laid both through the vertices, and through the edges. Input Set of triangles, given by coordinates of 3D-...
2
votes
0answers
2k views

Can Bellman-Ford run with time-complexity of cubic order

After reviewing the Bellman-Ford algorithm I can see that it runs with time complexity of $O(n^2)$ or, more exactly, $O(VE)$. It is necessary to loop (V-1) times the number of edges which is in fact 2 ...
2
votes
0answers
207 views

Why Johnson’s algorithm for all pairs shortest paths may create negative cycle?

There is a contradiction in the Johnson’s algorithm presented in CLRS edition 3 page 700 that I can't understand. Johnson’s algorithm uses the technique of reweighting, which works as follows: for ...
2
votes
0answers
478 views

Online version of bellman-ford algorithm?

Suppose I have a graph on which I've run the Bellman-Ford algorithm. Now I change the weight of subset of edges. Is there an efficient way to re-run the algorithm without having to completely start ...
2
votes
0answers
410 views

Bhandari Algorithm: Canceling Edges

I have a quick question on implementing the Bhandari algorithm. I do not have the textbook where the algorithm is originally given (Bhandari, Ramesh (1999). Survivable networks: algorithms for ...
2
votes
0answers
263 views

node-disjoint k-shortest path

As part of an object tracking application, I am trying to solve a node-disjoint k-shortest path problem. My graph is (for now) k-partite. I have a single source and single sink. My edges are initially ...
2
votes
0answers
398 views

Vectorized Algorithm for finding the Shortest Path in a Graph

I know that you can calculate the shortest path in a vectorized fashion using Floyd-Warshall, e.g. like proposed by Han and Kang, however I want the matrix, they call "via", the actual route taken ...
2
votes
0answers
60 views

How to compare A* with DP approach in finding shortest Path?

Consider a hypercube defined over $n$ dimensions where the edges are associated to strictly positive weights, and nodes are marked with $n$ bit-strings, e.g. the source is marked as (0,0,0) in a 3-...
2
votes
0answers
593 views

Does dijkstra works when I multiply weights of successive nodes

Consider a complete bidirectional weighted graph. Weight of each edge (a,b) is the probability of getting from a to b. So all weights are in range (0,1]. Probability of going from ...
2
votes
0answers
164 views

Update SSSPP solution on complete digraph on weight changes

I have a directed graph with $N$ vertices. Every pair of vertices is connected by two edges (one in each direction), and each of these edges has a weight which may be negative. On various occasions '...
2
votes
0answers
147 views

Multicommodity shortest path problem on a directed acyclic graph

I have n commodities with each a unique source and sink node. Each source-sink pair is connected in some manner on a directed acyclic graph. All arc weights are non-negative. The goal is to find the ...
2
votes
1answer
222 views

Linear time algorithm for finding $k$ shortest paths in unweighted graphs

Definition. Given an unweighted graph $G=(V,E)$ and two vertices $s$ and $t$, the $k$-shortest-paths problem is finding the $k$ shortest simple paths between $s$ and $t$ in $G$. Note that the ...
1
vote
0answers
11 views

Queries on unbounded knapsack

Given $n$ types of items with integer cost $c_{i}$ (there is an unlimited number of items of each type), such that $c_{i} \leq c$ for all $i = 1, 2, \dots, n$, answer (a lot of) queries of form "is ...
1
vote
0answers
16 views

Finding multiple paths through a grid such that every grid square is equally used

Setup Here’s the setup: I have an $N$ x $N$ grid of tiles, and a list of $M$ agents that need to move across the grid. Each agent has its own start tile $S(a)$, end tile $E(a)$, and an exact number ...
1
vote
1answer
29 views

A pathfinding algorithm for graphs in which arc weights can change over time

So I'm not really sure even what to be googling for solutions to this. Hence this question, hopefully, someone can point me in the right direction. Here's the situation, I have a weighted undirected ...
1
vote
0answers
148 views

Remove a vertex from a graph keeping shortest path distance same

How could we delete an arbitrary vertex from a directed weighted graph without changing the shortest-path distance between any other pair of vertices? We are allowed to reweight the edges.
1
vote
0answers
123 views

C++ finding the shortest path, reducing time complexity, dijkstra v Floyd Warshall Algorithm?

I have an algorithm that I am performing on a graph and I am looking to do an analysis of how to speed it up and would appreciate any comments. The algorithm iterates over every edge in the graph. ...
1
vote
0answers
48 views

Can the shortest path problem be solved using Monte Carlo Tree Search?

I think Monte Carlo Tree Search could be used to find the shortest path, but it seems that this method is only used considering win/lose outcomes in the simulation step. If we consider the path ...