Efficient shortest distance query processing and indexing on large road network

University of Technology Sydney. Faculty of Engineering and Information Technology.Computing the shortest distance between two vertices is a fundamental problem on road networks. State-of-the-art indexing-based solutions can be categorized into hierarchy-based solutions and hop-based solutions. However, the hierarchy-based solutions require a large search space for long-distance queries while the hop-based solutions result in a high computational waste for short-distance queries. Moreover, in real life, the weight of edges changes frequently. For example, building a road need several months, but the travel time of road changes frequently such as traffic jam in the morning peak. We model this problem as the shortest path problem on a dynamic road network. The existing solutions are not efficient to update the index for the dynamic condition. Shor-test path query on bicriteria road network is another important and practical problem in real life. To compute shortest path between any two vertices, we can get the shortest path set which is called path skyline. We propose an efficient exploring strategy to accelerate path skyline computing. We propose a novel hierarchical 2-hop index (H2H-Index) which assigns a label for each vertex and at the same time preserves a hierarchy among all vertices. With the H2H-Index, we design an efficient query processing algorithm with performance guarantees by visiting part of the labels for the source and destination based on the vertex hierarchy. We also propose an algorithm to construct the H2H-Index based on distance preserved graphs. The algorithm is further optimized by computing the labels based on the partially computed labels of other vertices. We use dynamic road network to define the graph model whose topological structure is stable and weight of edges changes frequently. In this model, we have two processing, shortest path query and road update processing, to do on road network. We use Contraction Hierarchies which is one of art-of-the-state index algorithm for shortest path problem to answer queries. And propose an efficient index updating algorithm to update CH index for road updating processing. In contrast to vertex centric algorithm, our shortcut centric algorithm has better theoretical bound. In the literature, PSQ is a fundamental algorithm for path skyline query and is also used as a building block for the afterwards proposed algorithms. In PSQ, a key operation is to record the skyline paths for each node that is possible on the skyline paths from to . However, to obtain the skyline paths for , PSQ has to maintain other paths that are not skyline paths for , which makes PSQ inefficient. Motivated by this, in this chapter, we propose a new algorithm PSQ⁺ for the path skyline query. By adopting an ordered path exploring strategy, our algorithm can totally avoid the fruitless path maintenance problem in PSQ. We conducted extensive performance studies using large real road networks including the whole USA road network. The experimental results demonstrate that our approach can make significant improvement to every problem

A Distributed Solution for Efficient K Shortest Paths Computation over Dynamic Road Networks

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 constantly change over time, representing evolving traffic conditions. Very often such services have to process numerous KSP queries over large road networks at the same time, thus there is a pressing need to identify distributed solutions for this problem. However, most existing approaches are designed to identify KSPs on a static graph in a sequential manner, restricting their scalability and applicability in a distributed setting. We therefore propose KSP-DG, a distributed algorithm for identifying k-shortest paths in a dynamic graph. It is based on partitioning the entire graph into smaller subgraphs, and reduces the problem of determining KSPs into the computation of partial KSPs in relevant subgraphs, which can execute in parallel on a cluster of servers. A distributed two-level index called DTLP is developed to facilitate the efficient identification of relevant subgraphs. A salient feature of DTLP is that it indexes a set of virtual paths that are insensitive to varying traffic conditions in an efficient and compact fashion, leading to very low maintenance cost in dynamic road networks. This is the first treatment of the problem of processing KSP queries over dynamic road networks. Extensive experiments conducted on real road networks confirm the superiority of our proposal over baseline methods.Comment: A shorter version of this technical report has been accepted for publication as a regular paper in TKDE. arXiv admin note: substantial text overlap with arXiv:2004.0258

Recent Advances in Fully Dynamic Graph Algorithms

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

Efficient Label-Constrained Shortest Path Queries on Road Networks: A Tree Decomposition Approach

Computing the shortest path between two vertices is a fundamental problem in road networks. Most of the existing works assume that the edges in the road networks have no labels, but in many real applications, the edges have labels and label constraints may be placed on the edges appearing on a valid shortest path. Hence, we study the label-constrained shortest path queries in this paper. In order to process such queries efficiently, we adopt an index-based approach and propose a novel index structure, LSD-Index, based on tree decomposition. With LSD-Index, we design an efficient query processing algorithm with good performance guarantees. Moreover, we also propose an algorithm to construct LSD-Index and further improve the efficiency of index construction by exploiting the parallel computing techniques. We conduct extensive performance studies using large real road networks including the whole USA road network. Compared with the state-of-the-art approach, the experimental results demonstrate that our algorithm not only achieves up to 2 orders of magnitude speedup in query processing time but also consumes much less index space. Meanwhile, the indexing time is also competitive, especially that for the parallel index construction algorithm

Comparing Alternative Route Planning Techniques: A Comparative User Study on Melbourne, Dhaka and Copenhagen Road Networks

Many modern navigation systems and map-based services do not only provide the fastest route from a source location s to a target location t but also provide a few alternative routes to the users as more options to choose from. Consequently, computing alternative paths has received significant research attention. However, it is unclear which of the existing approaches generates alternative routes of better quality because the quality of these alternatives is mostly subjective. Motivated by this, in this paper, we present a user study conducted on the road networks of Melbourne, Dhaka and Copenhagen that compares the quality (as perceived by the users) of the alternative routes generated by four of the most popular existing approaches including the routes provided by Google Maps. We also present a web-based demo system that can be accessed using any internet-enabled device and allows users to see the alternative routes generated by the four approaches for any pair of selected source and target. We report the average ratings received by the four approaches and our statistical analysis shows that there is no credible evidence that the four approaches receive different ratings on average. We also discuss the limitations of this user study and recommend the readers to interpret these results with caution because certain factors may have affected the participants' ratings.Comment: Extended the user study to also include the road networks of Dhaka and Copenhagen (the previous version only had Melbourne road network

Scalable Algorithms for the Analysis of Massive Networks

Die Netzwerkanalyse zielt darauf ab, nicht-triviale Erkenntnisse aus vernetzten Daten zu gewinnen. Beispiele für diese Erkenntnisse sind die Wichtigkeit einer Entität im Verhältnis zu anderen nach bestimmten Kriterien oder das Finden des am besten geeigneten Partners für jeden Teilnehmer eines Netzwerks - bekannt als Maximum Weighted Matching (MWM). Da der Begriff der Wichtigkeit an die zu betrachtende Anwendung gebunden ist, wurden zahlreiche Zentralitätsmaße eingeführt. Diese Maße stammen hierbei aus Jahrzehnten, in denen die Rechenleistung sehr begrenzt war und die Netzwerke im Vergleich zu heute viel kleiner waren. Heute sind massive Netzwerke mit Millionen von Kanten allgegenwärtig und eine triviale Berechnung von Zentralitätsmaßen ist oft zu zeitaufwändig. Darüber hinaus ist die Suche nach der Gruppe von k Knoten mit hoher Zentralität eine noch kostspieligere Aufgabe. Skalierbare Algorithmen zur Identifizierung hochzentraler (Gruppen von) Knoten in großen Graphen sind von großer Bedeutung für eine umfassende Netzwerkanalyse. Heutigen Netzwerke verändern sich zusätzlich im zeitlichen Verlauf und die effiziente Aktualisierung der Ergebnisse nach einer Änderung ist eine Herausforderung. Effiziente dynamische Algorithmen sind daher ein weiterer wesentlicher Bestandteil moderner Analyse-Pipelines. Hauptziel dieser Arbeit ist es, skalierbare algorithmische Lösungen für die zwei oben genannten Probleme zu finden. Die meisten unserer Algorithmen benötigen Sekunden bis einige Minuten, um diese Aufgaben in realen Netzwerken mit bis zu Hunderten Millionen von Kanten zu lösen, was eine deutliche Verbesserung gegenüber dem Stand der Technik darstellt. Außerdem erweitern wir einen modernen Algorithmus für MWM auf dynamische Graphen. Experimente zeigen, dass unser dynamischer MWM-Algorithmus Aktualisierungen in Graphen mit Milliarden von Kanten in Millisekunden bewältigt.Network analysis aims to unveil non-trivial insights from networked data by studying relationship patterns between the entities of a network. Among these insights, a popular one is to quantify the importance of an entity with respect to the others according to some criteria. Another one is to find the most suitable matching partner for each participant of a network knowing the pairwise preferences of the participants to be matched with each other - known as Maximum Weighted Matching (MWM). Since the notion of importance is tied to the application under consideration, numerous centrality measures have been introduced. Many of these measures, however, were conceived in a time when computing power was very limited and networks were much smaller compared to today's, and thus scalability to large datasets was not considered. Today, massive networks with millions of edges are ubiquitous, and a complete exact computation for traditional centrality measures are often too time-consuming. This issue is amplified if our objective is to find the group of k vertices that is the most central as a group. Scalable algorithms to identify highly central (groups of) vertices on massive graphs are thus of pivotal importance for large-scale network analysis. In addition to their size, today's networks often evolve over time, which poses the challenge of efficiently updating results after a change occurs. Hence, efficient dynamic algorithms are essential for modern network analysis pipelines. In this work, we propose scalable algorithms for identifying important vertices in a network, and for efficiently updating them in evolving networks. In real-world graphs with hundreds of millions of edges, most of our algorithms require seconds to a few minutes to perform these tasks. Further, we extend a state-of-the-art algorithm for MWM to dynamic graphs. Experiments show that our dynamic MWM algorithm handles updates in graphs with billion edges in milliseconds

Cost allocation in connection and conflict problems on networks: a cooperative game theoretic approach

This thesis examines settings where multiple decision makers with conflicting interests benefit from cooperation in joint combinatorial optimisation problems. It draws on cooperative game theory, polyhedral theory and graph theory to address cost sharing in joint single-source shortest path problems and joint weighted minimum colouring problems. The primary focus of the thesis are problems where each agent corresponds to a vertex of an undirected complete graph, in which a special vertex represents the common supplier. The joint combinatorial optimisation problem consists of determining the shortest paths from the supplier to all other vertices in the graph. The optimal solution is a shortest path tree of the graph and the aim is to allocate the cost of this shortest path tree amongst the agents. The thesis defines shortest path tree problems, proposes allocation rules and analyses the properties of these allocation rules. It furthermore introduces shortest path tree games and studies the properties of these games. Various core allocations for shortest path tree games are introduced and polyhedral properties of the core are studied. Moreover, computational results on finding the core and the nucleolus of shortest path tree games for the application of cost allocation in Wireless Multihop Networks are presented. The secondary focus of the thesis are problems where each agent is interested in having access to a number of facilities but can be in conflict with other agents. If two agents are in conflict, then they should have access to disjoint sets of facilities. The aim is to allocate the cost of the minimum number of facilities required by the agents amongst them. The thesis models these cost allocation problems as a class of cooperative games called weighted minimum colouring games, and characterises total balancedness and submodularity of this class of games using the properties of the underlying graph