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Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network)…

The design of efficient transportation networks is an important challenge in many research areas. Among the most promising recent methods, biological routing mimic local rules found in nature. However comparisons with other methods are…

Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted…

Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing…

In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points source and destination, and it is not necessary to calculate the shortest path from source…

Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the…

Rapid urbanization places increasing stress on already burdened transportation systems, resulting in delays and poor levels of service. Billions of spatiotemporal call detail records (CDRs) collected from mobile devices create new…

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…

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide…

In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…

We study the problem of quickly computing point-to-point shortest paths in massive road networks with traffic predictions. Incorporating traffic predictions into routing allows, for example, to avoid commuter traffic congestions. Existing…

The structure of road networks impacts various urban dynamics, from traffic congestion to environmental sustainability and access to essential services. Recent studies reveal that most roads are underutilized, faster alternative routes are…

We present a novel algorithm to match GPS trajectories onto maps offline (in batch mode) using techniques borrowed from the field of force-directed graph drawing. We consider a simulated physical system where each GPS trajectory is…

Distributed consensus has been intensively studied in recent years as a means to mitigate state differences among dynamic nodes on a graph. It has been successfully employed in various applications, e.g., formation control of multi-robots,…

Mode connectivity is a phenomenon where trained models are connected by a path of low loss. We reframe this in the context of Information Geometry, where neural networks are studied as spaces of parameterized distributions with curved…

Finding the shortest path between two points in a graph is a fundamental problem that has been well-studied over the past several decades. Shortest path algorithms are commonly applied to modern navigation systems, so our study aims to…

The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…

Finding the shortest paths in road network is an important query in our life nowadays, and various index structures are constructed to speed up the query answering. However, these indexes can hardly work in real-life scenario because the…

We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly…

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…