相关论文: The Covering Path Problem on a Grid
The isometric path cover (partition) problem of a graph is to find a minimum set of isometric paths which cover (partition) the vertex set of the graph. The isometric path cover (partition) number of a graph is the cardinality a minimum…
We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our…
We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time;…
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts the performance of the SBBU algorithm for protein structure…
The GC problem is to identify a pre-determined number of center vertices such that the distances or costs from (or to) the centers to (or from) other vertices is minimized. The bottleneck of a path is the minimum capacity of edges on the…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
Narrow passage path planning is a prevalent problem from industrial to household sites, often facing difficulties in finding feasible paths or requiring excessive computational resources. Given that deep penetration into the environment can…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the…
Line coverage is the task of servicing a given set of one-dimensional features in an environment. It is important for the inspection of linear infrastructure such as road networks, power lines, and oil and gas pipelines. This paper…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
This paper investigates the problem of computing the shortest path between two states under resource constraints in environments with resource-replenishment regions. Namely, the length of the path is limited by a budget that can be restored…
Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…
In practice, navigation of mobile robots in confined environments is often done using a spatially discrete cost-map to represent obstacles. Path following is a typical use case for model predictive control (MPC), but formulating constraints…
We consider the bi-criteria shortest-path problem where we want to compute shortest paths on a graph that simultaneously balance two cost functions. While this problem has numerous applications, there is usually no path minimizing both cost…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
In high-density environments where numerous autonomous agents move simultaneously in a distributed manner, streamlining global flows to mitigate local congestion is crucial to maintain overall navigation efficiency. This paper introduces a…
Given a graph $G$ rooted at a vertex $r$ and weight functions, $\gamma, \tau: E(G) \rightarrow \mathbb{R}$, the generalized cable-trench problem (CTP) is to find a single spanning tree that simultaneously minimizes the sum of the total edge…