Despite the importance of spatial networks in real-life applications, most of the spatial database literature focuses on Euclidean spaces. In this paper we propose an architecture that integrates network and Euclidean information, capturing pragmatic constraints. Based on this architecture, we develop a Euclidean restriction and a network expansion framework that take advantage of location and connectivity to efficiently prune the search space. These frameworks are successfully applied to the most popular spatial queries, namely nearest neighbors, range search, closest pairs and e-distance joins, in the context of spatial network databases.

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Query processing in spatial network databases

The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the time-dependent shortest-path problem. A time-dependent graph GT is a graph that has an edge-delay function, wi, j(t), associated with each edge (vi, vj), to be stored in a database. The edge-delay function wi, j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A user-specified query is to ask the minimum-travel-time path, from a source node, vs, to a destination node, ve, over the time-dependent graph, GT, with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT. The challenge of this problem is the added complexity due to the time dependency in the time-dependent graph. That is, edge delays are not constants, and can vary from time to time. In this paper, we propose a novel algorithm to find the minimum-travel-time path with the best departure time for a LTT(vs, ve, T) query over a large graph GT. Our approach outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice. We will discuss the design of our algorithm, together with its correctness and complexity. We conducted extensive experimental studies over large graphs and will report our findings.

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Finding time-dependent shortest paths over large graphs

This paper proposes and solves the Time-Interval All Fastest Path (allFP) query. Given a user-defined leaving or arrival time interval I, a source node s and an end node e, allFP asks for a set of all fastest paths from s to e, one for each sub-interval of I. Note that the query algorithm should find a partitioning of I into sub-intervals. Existing methods can only be used to solve a very special case of the problem, when the leaving time is a single time instant. A straightforward solution to the allFP query is to run existing methods many times, once for every time instant in I. This paper proposes a solution based on novel extensions to the A* algorithm. Instead of expanding the network many times, we expand once. The travel time on a path is kept as a function of leaving time. Methods to combine travel-time functions are provided to expand a path. A novel lower-bound estimator for travel time is proposed. Performance results reveal that our method is more efficient and more accurate than the discrete-time approach.

/pdf/finding-fastest-paths-on-a-road-network-with-speed-patterns-3i1qpen9e4.pdf

Finding Fastest Paths on A Road Network with Speed Patterns

Current spatial database management systems (SDBMS) provide efficient access methods and operators for point and range queries over collections of spatial points, line segments, and polygons. However, it is not clear if existing spatial access methods can efficiently support network computations which traverse line segments in a spatial network based on connectivity rather than geographic proximity. The expected I/O cost for many network operations can be reduced by maximizing the Weighted Connectivity Residue Ratio (WCRR), i.e., the chance that a pair of connected nodes that are more likely to be accessed together are allocated to a common page of the file. CCAM is an access method for general networks that uses connectivity clustering. CCAM supports the operations of insert, delete, create, and find as well as the new operations, get-A-successor and get-successors, which retrieve one or all successors of a node to facilitate aggregate computations on networks. The nodes of the network are assigned to disk pages via a graph partitioning approach to maximize the WCRR. CCAM includes methods for static clustering, as well as dynamic incremental reclustering, to maintain high WCRR in the face of updates, without incurring high overheads. We also describe possible modifications to improve the WCRR that can be achieved by existing spatial access methods. Experiments with network computations on the Minneapolis road map show that CCAM outperforms existing access methods, even though the proposed modifications also substantially improve the performance of existing spatial access methods.

/pdf/ccam-a-connectivity-clustered-access-method-for-networks-and-1qmxyct7kj.pdf

CCAM: a connectivity-clustered access method for networks and network computations

Several graph-based algorithms have been proposed in the literature to compute the transitive closure of a directed graph. We develop two new algorithms (Basic_TC and Gobal_DFTC) and compare the performance of their implementations in a disk-based environment with a well-known graph-based algorithm proposed by Schmitz. Our algorithms use depth-first search to traverse a graph and a technique called marking to avoid processing some of the arcs in the graph. They compute the closure by processing nodes in reverse topological order, building descendent sets by adding the descendent sets of children. While the details of these algorithms differ considerably, one important difference among them is the time at which descendent set additions are performed. Basic_TC, results in superior performance. The first reason is that early additions result in larger descendent set sizes on the average over the duration of the execution, thereby causing more I/O; very often this turns out to more than offset the gains of not having to fetch certain sets again to add them. The second reason is that information collected in the first pass can be used to apply several optimizations in the second pass. To the extent possible, we also adapt these algorithms to perform path computations. Again, our performance comparison confirms the trends seen in reachability queries. Taken in conjunction with another performance study our results indicate that all graph-based algorithms significantly outperform other types of algorithms such as Seminaive and Warren.

Transitive closure algorithms based on graph traversal

To establish the behavior of algorithms in a paging environment, the author analyzes the input/output (I/O) efficiency of several representative shortest path algorithms. These algorithms include single-course, multisource, and all pairs ones. The results are also applicable for other path problems such as longest paths, most reliable paths, and bill of materials. The author introduces the notation and a model of a paging environment. The I/O efficiencies of the selected single-source, all pairs, and multisource algorithms are analyzed and discussed. >

Bin Jiang

Papers

I/O-efficiency of shortest path algorithms: an analysis