Dynamic Shortest Paths Containers

Journal of Experimental Algorithmics, 2005

Speed-up techniques that exploit given node coordinates have proven useful for shortest-path computations in transportation networks and geographic information systems. To facilitate the use of such techniques when coordinates are missing from some, or even all, of the nodes in a network we generate artificial coordinates using methods from graph drawing. Experiments on a large set of German train timetables indicate that the speed-up achieved with coordinates from our drawings is close to that achieved with the true coordinates-and in some special cases even better.

Journal of Experimental Algorithmics, 2005

Computing a shortest path from one node to another in a directed graph is a very common task in practice. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality of the solution can still be guaranteed. In most studies, such techniques are considered individually. The focus of our work is combination of speed-up techniques for Dijkstra's algorithm. We consider all possible combinations of four known techniques, namely goaldirected search, bidirectional search, multi-level approach, and shortest-path containers, and show how these can be implemented. In an extensive experimental study we compare the performance of the various combinations and analyze how the techniques harmonize when applied jointly. Several real-world graphs from road maps and public transport and three types of generated random graphs are taken into account.

International Transactions in Operational Research, 2008

Among the variants of the well known shortest path problem, those that refer to a dynamically changing graphs are theoretically interesting, as well as computationally challenging. Applicationwise, there is an industrial need for computing point-to-point shortest paths on large-scale road networks whose arcs are weighted with a travelling time which depends on traffic conditions. We survey recent techniques for dynamic graph weights as well as dynamic graph topology.

Computing Research Repository, 2010

This paper considers the problem of finding a quickest path between two points in the Euclidean plane in the presence of a transportation network. A transportation network consists of a planar network where each road (edge) has an individual speed. A traveller may enter and exit the network at any point on the roads. Along any road the traveller moves with a fixed speed depending on the road, and outside the network the traveller moves at unit speed in any direction. We give an exact algorithm for the basic version of the problem: given a transportation network of total complexity n in the Euclidean plane, a source point s and a destination point t, and the quickest path between s and t. We also show how the transportation network can be preprocessed in time O(n^2 log n) into a data structure of size O(n^2) such that (1 + \epsilon)-approximate cheapest path cost queries between any two points in the plane can be answered in time O(1\epsilon^4 log n).

2014

Computing the shortest path between two locations in a road network is an important problem that has found numerous applications. The classic solution for the problem is Dijkstra’s algorithm [1]. Although simple and elegant, the algorithm has proven to be inefficient for very large road networks. To address this deficiency of Dijkstra’s algorithm, a plethora of techniques that introduce some preprocessing to reduce the query time have been proposed. In this paper, we propose Partition-based Shortcuts (PbS), a technique based on graph-partitioning which offers fast query processing and supports efficient edge weight updates. We present a shortcut computation scheme, which exploits the traits of a graph partition. We also present a modified version of the bidirectional search [2], which uses the precomputed shortcuts to efficiently answer shortest path queries. Moreover, we introduce the Corridor Matrix (CM), a partition-based structure which is exploited to reduce the search space du...

2000

Determining the shortest path from one node to another in a graph is probably the most popular question in graph theory. If the graph is non-negatively weighted, Dijkstra's algorithm is the classic algorithm used to answer this question. Because of its breadth-first-search character, this algorithm usually spreads circularly around the source node of the search and hence the search space can be very large. For the application of dealing with huge numbers of shortest-path queries in static graphs, we consider an algorithm, which uses preprocessed data to decrease the search space for each shortest-path request. The algorithm partitions the graph and, for each edge, the preprocessing considers the relevant regions which have the shortest path over this edge. We will see that the preprocessing scales well and usually runs in almost linear time.

PROMET - Traffic&Transportation, 2014

In the field of geoinformation and transportation science, the shortest path is calculated on graph data mostly found in road and transportation networks. This data is often stored in various database systems. Many applications dealing with transportation network require calculation of the shortest path. The objective of this research is to compare the performance of Dijkstra shortest path calculation in PostgreSQL (with pgRouting) and Neo4j graph database for the purpose of determining if there is any difference regarding the speed of the calculation. Benchmarking was done on commodity hardware using OpenStreetMap road network. The first assumption is that Neo4j graph database would be well suited for the shortest path calculation on transportation networks but this does not come without some cost. Memory proved to be an issue in Neo4j setup when dealing with larger transportation networks.

Journal of the ACM, 1990

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap , is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C , a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O ( m + n log C ). A two-level form of radix heap gives a bound of O ( m + n log C /log log C ). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O ( m + n a @@@@log C ). The best previously known bounds are O ( m + n log n ) using Fibonacci heaps alone and O ( m log log C ) using the priority queue structure of Van Emde Boas et al. [ 17].

Synthesis Lectures on Theoretical Computer Science, 2014

Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology.

2016 17th IEEE International Conference on Mobile Data Management (MDM), 2016

Computing the shortest path between two locations in a road network is an important problem that has found numerous applications. The classic solution for the problem is Dijkstra's algorithm [1]. Although simple and elegant, the algorithm has proven to be inefficient for very large road networks. To address this deficiency of Dijkstra's algorithm, a plethora of techniques that introduce some preprocessing to reduce the query time have been proposed. In this paper, we propose Partition-based Shortcuts (PbS), a technique based on graph-partitioning which offers fast query processing and supports efficient edge weight updates. We present a shortcut computation scheme, which exploits the traits of a graph partition. We also present a modified version of the bidirectional search [2], which uses the precomputed shortcuts to efficiently answer shortest path queries. Moreover, we introduce the Corridor Matrix (CM), a partition-based structure which is exploited to reduce the search space during the processing of shortest path queries when the source and the target point are close. Finally, we evaluate the performance of our modified algorithm in terms of preprocessing cost and query runtime for various graph partitioning configurations.