Related papers: Faster Goal-Oriented Shortest Path Search for Bulk…
Decentralized optimization with orthogonality constraints is found widely in scientific computing and data science. Since the orthogonality constraints are nonconvex, it is quite challenging to design efficient algorithms. Existing…
We describe a new forward-backward variant of Dijkstra's and Spira's Single-Source Shortest Paths (SSSP) algorithms. While essentially all SSSP algorithm only scan edges forward, the new algorithm scans some edges backward. The new…
We consider several basic questions on distributed routing in directed graphs with multiple additive costs, or metrics, and multiple constraints. Distributed routing in this sense is used in several protocols, such as IS-IS and OSPF. A…
We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph $G$ on $n$ vertices can be partitioned into a set of $O(n/r)$ edge-disjoint regions (called an $r$-division) with $O(r)$ vertices each,…
In this work we consider algorithms for reconstructing time-varying data into a finite sum of discrete trajectories, alternatively, an off-the-grid sparse-spikes decomposition which is continuous in time. Recent work showed that this…
Deep learning approaches have shown promising results in solving routing problems. However, there is still a substantial gap in solution quality between machine learning and operations research algorithms. Recently, another line of research…
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…
We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art…
Motivated by the increasing availability of vehicle trajectory data, we propose learn-to-route, a comprehensive trajectory-based routing solution. Specifically, we first construct a graph-like structure from trajectories as the routing…
It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…
Path planning plays a crucial role in various autonomy applications, and RRT* is one of the leading solutions in this field. In this paper, we propose the utilization of vertex-based networks to enhance the sampling process of RRT*, leading…
We study the problem of computing isochrones in road networks, where the objective is to identify the region that is reachable from a given source within a certain amount of time. While there is a wide range of practical applications for…
The problem of identifying the k-shortest paths KSPs for short in a dynamic road network is essential to many location-based services. Road networks are dynamic in the sense that the weights of the edges in the corresponding graph…
We propose a throughput-optimal biased backpressure (BP) algorithm for routing, where the bias is learned through a graph neural network that seeks to minimize end-to-end delay. Classical BP routing provides a simple yet powerful…
In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
This paper addresses the problem of finding multiple near-optimal, spatially-dissimilar paths that can be considered as alternatives in the decision making process, for finding optimal corridors in which to construct a new road. We further…
Generic Dijkstra is a novel algorithm for finding the optimal shortest path in both wavelength-division multiplexed networks (WDM) and elastic optical networks (EON), claimed to outperform known algorithms considerably. Because of its…
We study efficient and exact shortest path algorithms for routing on road networks with realistic traffic data. For navigation applications, both current (i.e., live) traffic events and predictions of future traffic flows play an important…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…