# Questions tagged [shortest-path]

The tag has no usage guidance.

68 questions
Filter by
Sorted by
Tagged with
292 views

### Recent progress on the next-to-shortest-path problem for directed graphs?

In the paper "Computing strictly-second shortest paths" (1997), Lalgudi and Papaefthymiou consider the following problem: Let $G$ be a directed graph with edge-weighting $w$. Let $u,v$ be vertices in ...
28 views

### Optimum first stage solution of two stage stochastic shortest path induces tree

I struggle with the proof of Lemma 1 in the Paper "Hedging Uncertainty: Approximation Algorithms for Stochastic Optimization Problems" by Ravi and Sinha and hope this is the right community ...
36 views

### Multi agent path following with collision avoidance with pre-determined path

I am working on a multi-agent pathfinding algorithm. I am aware of other techniques, but planned on the folowing strategy only. The problem: There is 12x12 grid, with a few solid blockades within them....
193 views

### Shortest path on a hypergraph with no leftovers

In quantum computing, determining the code distance of a stabilizer code is similar to the shortest path problem on a hypergraph. Each node in the graph would be some sort of parity check performed by ...
133 views

### Is APSP verification easier than APSP?

In APSP, the input is an $n$-node directed weighted graph $G$, and the output is an $n \times n$ matrix holding pairwise shortest path distances between nodes in $G$. Define "APSP-Verification" as ...
49k views

### How do the state-of-the-art pathfinding algorithms for changing graphs (D*, D*-Lite, LPA*, etc) differ?

A lot of pathfinding algorithms have been developed in recent years which can calculate the best path in response to graph changes much faster than A* - what are they, and how do they differ? Are ...
482 views

### Dijkstra parallelization

I'd like to know what is the best method to parallelize the Dijkstra algorithm. Thanks.
644 views

### What about apply maxplus algebra for all-pairs shortest paths?

I didn't find deep informations on Wikipedia about all-pairs shortest path, in particular I do not know what is the best algorithm to solve this problem beyond Floyd-Warshall's one, then I do not know ...
293 views

### Find the shortest s-t trail(edge disjoint path) in a graph with negative weight edges

A walk in a graph is a finite or infinite sequence of edges which joins a sequence of vertices. A trail is a walk in which all edges are distinct. Note that a trial may visit a vertex multiple times ...
1k views

### directed or bidirected in relation to mssp (Multiple source shortest path)

Firstly I wanted to ask. If I have a undirected graph and split all the edges into two directed edges is it still called directed or does it become bi-directed? The main question is i have a graph ...
2k views

### Number of simple paths between two vertices in a DAG

Let $G = (N, A)$ be a connected acyclic digraph (DAG). Furthermore, let $s \in N$ and $t \in N$ be two vertices on this graph, such that $t$ is reachable from $s$. My problem is: how many simple $s-t$...
762 views

### Graph classes for which the diameter can be computed in linear time

Recall the diameter of a graph $G$ is the length of a longest shortest path in $G$. Given a graph, an obvious algorithm for computing $\text{diam}(G)$ solves the all-pairs shortest path problem (APSP) ...
477 views

### Minimum Union-Sum Cost Path

I have a minimum cost path selection problem that is different from the usual shortest path in that each type of cost is accounted only once in the total cost of the path if multiple edges on the path ...
101 views

### Bellman-Ford with Non-edge-decomposable Path Weights

Consider a directed graph $G(V,E)$ with non-negative edge weights. Also, let us define the weight of a path as non-edge-decomposable, that is, the weight of a path cannot be written as the sum of a ...
159 views

### When is extra vertex required in arbitrage detection using Bellman Ford?

I am studying applications of shortest path, in particular arbitrage. Specifically, I was reading these two resources: https://stackoverflow.com/questions/2282427/interesting-problem-currency-...
140 views

### Finding Cheapest n-Path [closed]

Given a weighted directed acyclic graph, how can I find the cheapest path from an Origin Vertex to a Destination Vertex which ...
5k views

### Combinatorics of Bellman-Ford or how to make cyclic graphs acyclic?

Roughly speaking, my question is: How costly is to make a cyclic graph acyclic while preserving all simple $s$-$t$ paths? Let $K_n$ be a complete undirected graph on vertices $\{0,1,\ldots,n+1\}$. (...
269 views

### Finding shortest path while maximizing the number of overlapping edges

The shortest path problem between 2 arbitrary nodes is one that has been covered extensively and the solution is well-known. Consider the edge costs to be arbitrary. Consider the following variant: ...
481 views

### What exactly is Lawler's modification to Yen's algorithm and how does it work?

I recently read about Yen's algorithm, I understand the algorithm and it seems correct, however Wikipedia mentions that there exists "Lawler's modification" to the algorithm, which is described as ...
519 views

### Maximum difference between two shortest paths

My problem is the following maximization problem: Given: A graph $G=(V,E)$, lower bounds $l \in \{0,1,..,K\}^E$ and upper bound $u \in \{0,1,..,K\}^E$ for the edge weights, a source $s$ and two ...
8k views

181 views

### Are there any heuristics that works solely on graphs?

I'm exploring heuristics in A* and apparently all heuristics require coordinates of all the locations to calculate a h-cost. This is fine if you are working on grids, but what if you need to work ...
538 views

### Path finding on graph with state dependent edge costs

I'm looking for a version of path planning that is able to find paths in a graph where edge costs depend on the state of the moving entity. In such cases, it is required to also consider trade-offs, i....
297 views

### Ref question: K-nearest neighbours in a graph

Given an undirected graph $G$ with $n$ vertices, $m$ edges, and positive weights on the edges, I am interested in the problem of computing for each vertex the $k$ distinct vertices in $G$ that are ...
85 views

### Constant Width Max Sum Product Multi-objective Shortest path problem

This question is a follow-up on the question I asked three days ago here. For convenience I restate it here. I am given a graph. Each edge is labelled by a vector of numbers, called weights. They ...
207 views

### Max Sum Product Multi-objective Shortest path problem

Is anything known about the following problem: I am given a graph. Each edge is labelled by a vector of numbers, called weights. They are numbers between 0 and 1. A path is first assigned a vector, ...
86 views

### Cooperative Pathfinding to minimize global costs

There are some algorithms and methods around, that allow cooperative pathfinding. Unfortunately they all seem to aim at avoiding collisions or conflicts between entities. I'm looking for an algorithm ...
418 views

### Why is label pruning possible with hub labeling?

Hub labeling (HL) computes superlabels using the vertices visited by the forward and reverse Contraction Hierarchies (CH) search. Those labels are then pruned (see HL, sec. 4.2) to generate strict ...
548 views

### Shortest non-crossing geometric paths

I have a plane graph $G$ and a set of $k$ vertex pairs $\{s_1,t_1\}, \dots, \{s_k, t_k\}$. The goal is to find $k$ non-crossing paths connecting the pairs of terminals $s_i$ with $t_i$ in the graph so ...
182 views

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 $c_{... 0answers 82 views ### In a shortest path between two nodes, find if a certain node is unique So my exact problem is, I have to find if there is any node which is unique in a shortest path. For example, in a square, any node is in the shortest path between any two adjacent nodes,but it is not ... 2answers 2k views ### Finding the two shortest paths while minimizing the number of nearby/common edges The shortest path problem between 2 arbitrary nodes is one that has been covered extensively and the solution is well-known. Consider the edge costs to be arbitrary. Consider the following variant: ... 0answers 468 views ### Dynamic shortest path data structure for DAG Let$G$be a dynamic DAG (directed acyclic graph) where new vertices and new edges can be inserted. I am looking for an efficient data structure/algorithm to maintain the shortest path from a fixed ... 0answers 209 views ### Efficiently computing propagation values for only a few positions in a grid Consider a matrix filled with some nodes containing positive integers ("starts"), some nodes marked as a wall, and the rest of the nodes given a value of infinity. The propogation rule is simple: For ... 1answer 704 views ### Highway dimension I'm interested in understanding some recent theoretical results on pathfinding. Specifically this paper: http://research.microsoft.com/apps/pubs/default.aspx?id=201061 I understand from the paper ... 0answers 901 views ### Lower bounds on single-source shortest paths in directed graphs Are there any non-trivial lower bounds on the complexity of single-source shortest paths (SSSP) in a directed graph, where all edges have non-negative edge weights? Can we rule out the possibility of ... 2answers 3k views ### Shortest path hitting a given vertex I believe this problem to be NP-Complete, but I'm unable to find any references on possible reductions. Given a weighted graph (either undirected or directed, I cannot find results for either but am ... 1answer 1k views ### Identifying useless edges for shortest path Consider a graph$G$(the problem makes sense both for directed and undirected graphs). Call$M_G$the matrix of distances of$G$:$M_G[i, j]$is the shortest path distance from vertex$i$to vertex$...
Given an unweighted tree $T=(V,E)$ what is the minimum number of distance oracles that allow to detect the position in the graph of every node $v$? A distance oracle is "special node" $u$ of the ...