Questions tagged [shortest-path]

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

105 questions with no upvoted or accepted answers
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11
votes
0answers
517 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
257 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
181 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
326 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
422 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
517 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
1answer
47 views

Conditional lower bounds on the running time of the single source shortest path problem

Just out of curiosity, I was wondering whether there is a conditional lower-bound on the running time of an algorithm for the Single Source Shortest Path Problem (on directed or undirected graphs). I ...
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
688 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
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0answers
144 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
124 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
votes
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
661 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
121 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
79 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
410 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
315 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
918 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
327 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
17 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
43 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
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
85 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
votes
0answers
169 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
votes
0answers
130 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
110 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
36 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
348 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
266 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. $...
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
194 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
394 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 ...
2
votes
0answers
448 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
370 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
246 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
372 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
59 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
572 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
124 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
218 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
95 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
29 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 ...
1
vote
1answer
83 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, ...
1
vote
0answers
39 views

Concurrent Shortest Paths with “Congestion Penalty”

Given a graph with positive edge weight representing "time to travel through", and 2 or more pairs of start/end vertices, we can find concurrent paths for the pairs such that the maximum cumulative ...