Related papers: Finding k-Dissimilar Paths with Minimum Collective…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during…
The detection of curved lanes is still challenging for autonomous driving systems. Although current cutting-edge approaches have performed well in real applications, most of them are based on strict model assumptions. Similar to other…
The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We…
Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables,…
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,…
We study the problem of finding, in a directed graph, an st-walk of length r mod q which is edge-minimum, i.e., uses the smallest number of distinct edges. Despite the vast literature on paths and cycles with modularity constraints, to the…
We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…
We present a new approach called GR (Graph Reduction) algorithm for searching loop-less k-shortest paths (1st to k-th shortest paths) in a graph based on graph reduction. Let a source vertex and a target vertex of k-shortest paths be v_s…
Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…
In minimum power network design problems we are given an undirected graph $G=(V,E)$ with edge costs $\{c_e:e \in E\}$. The goal is to find an edge set $F\subseteq E$ that satisfies a prescribed property of minimum power $p_c(F)=\sum_{v \in…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
The Dijkstra algorithm is a classic path planning method, which in a discrete graph space, can start from a specified source node and find the shortest path between the source node and all other nodes in the graph. However, to the best of…
In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…
One of the most fundamental graph problems is finding a shortest path from a source to a target node. While in its basic forms the problem has been studied extensively and efficient algorithms are known, it becomes significantly harder as…
In train routing, the headway is the minimum distance that must be maintained between successive trains for safety and robustness. We introduce a model for train routing that requires a fixed headway to be maintained between trains, and…
Due to the vastly different energy consumption between up-slope and down-slope, a path with the shortest length on a complex off-road terrain environment (2.5D map) is not always the path with the least energy consumption. For any…
In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…
Simplicial complexes are extensively studied in the field of algebraic topology. They have gained attention in recent time due to their applications in fields like theoretical distributed computing and simplicial neural networks. Graphs are…