Related papers: Computing shortest paths in 2D and 3D memristive n…

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

Path planning is crucial for the efficient operation of Autonomous Mobile Robots (AMRs) in factory environments. Many existing algorithms rely on Dubins paths, which have been adapted for various applications. However, an efficient method…

Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many…

In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. This algorithm can be considered as an improvement of [13]. Then based on this sequential algorithm, we present a constant-time parallel…

Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the…

Considering a graph with unknown weights, can we find the shortest path for a pair of nodes if we know the minimal Steiner trees associated with some subset of nodes? That is, with respect to a fixed latent decision-making system (e.g., a…

The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms that only evaluate edges along shortest paths between the source and target. These algorithms were designed to minimize the number of edge evaluations in settings…

We demonstrate that challenging shortest path problems can be solved via direct spline regression from a neural network, trained in an unsupervised manner (i.e. without requiring ground truth optimal paths for training). To achieve this, we…

Alternative paths in a network play an important role in its functionality as they can maintain the information flow under node/link failures. In this paper we explore the navigation of a network taking into account the alternative paths…

This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a…

The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…

In this paper, we present a novel learning framework for finding shortest paths in graphs utilizing Generative Flow Networks (GFlowNets). First, we examine theoretical properties of GFlowNets in non-acyclic environments in relation to…

It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure…

For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are…

Shortest path problems are a touchstone for evaluating the computing performance and functional range of novel computing substrates. Much has been published in recent years regarding the use of biocomputers to solve minimal path problems…

We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…

Network flow is a powerful mathematical framework to systematically explore the relationship between structure and function in biological, social, and technological networks. We introduce a new pipelining model of flow through networks…

We show that neural networks can be optimized to represent minimum energy paths as continuous functions, offering a flexible alternative to discrete path-search methods such as Nudged Elastic Band (NEB). Our approach parameterizes reaction…

We study the NP-hard Shortest Path Most Vital Edges problem arising in the context of analyzing network robustness. For an undirected graph with positive integer edge lengths and two designated vertices $s$ and $t$, the goal is to delete as…

The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…