Route Planning in Transportation Networks

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 different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Applications of graph algorithms in GIS

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Leveraging Semantic Web Technologies for Managing Resources in a Multi-Domain Infrastructure-as-a-Service Environment

This paper reports on experience with using semantically-enabled network resource models to construct an operational multi-domain networked infrastructure-as-a-service (NIaaS) testbed called ExoGENI, recently funded through NSF's GENI project. A defining property of NIaaS is the deep integration of network provisioning functions alongside the more common storage and computation provisioning functions. Resource provider topologies and user requests can be described using network resource models with common base classes for fundamental cyber-resources (links, nodes, interfaces) specialized via virtualization and adaptations between networking layers to specific technologies. This problem space gives rise to a number of application areas where semantic web technologies become highly useful - common information models and resource class hierarchies simplify resource descriptions from multiple providers, pathfinding and topology embedding algorithms rely on query abstractions as building blocks. The paper describes how the semantic resource description models enable ExoGENI to autonomously instantiate on-demand virtual topologies of virtual machines provisioned from cloud providers and are linked by on-demand virtual connections acquired from multiple autonomous network providers to serve a variety of applications ranging from distributed system experiments to high-performance computing

Grammar-Based Geodesics in Semantic Networks

A geodesic is the shortest path between two vertices in a connected network. The geodesic is the kernel of various network metrics including radius, diameter, eccentricity, closeness, and betweenness. These metrics are the foundation of much network research and thus, have been studied extensively in the domain of single-relational networks (both in their directed and undirected forms). However, geodesics for single-relational networks do not translate directly to multi-relational, or semantic networks, where vertices are connected to one another by any number of edge labels. Here, a more sophisticated method for calculating a geodesic is necessary. This article presents a technique for calculating geodesics in semantic networks with a focus on semantic networks represented according to the Resource Description Framework (RDF). In this framework, a discrete "walker" utilizes an abstract path description called a grammar to determine which paths to include in its geodesic calculation. The grammar-based model forms a general framework for studying geodesic metrics in semantic networks.Comment: First draft written in 200

The Minimum Wiener Connector

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph $G=(V,E)$ and a set $Q\subseteq V$ of query vertices, find a subgraph of $G$ that connects all query vertices and has minimum Wiener index. We show that The Minimum Wiener Connector admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless $\mathbf{P} = \mathbf{NP}$. Our main contribution is a constant-factor approximation algorithm running in time $\widetilde{O}(|Q||E|)$. A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set $Q$ a small number of important vertices (i.e., vertices with high centrality).Comment: Published in Proceedings of the 2015 ACM SIGMOD International Conference on Management of Dat