Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Fully dynamic output bounded single source shortest path problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
Fully dynamic algorithms for maintaining shortest paths trees
Journal of Algorithms
An Efficient Path Computation Model for Hierarchically Structured Topographical Road Maps
IEEE Transactions on Knowledge and Data Engineering
Improved Distance Oracles for Avoiding Link-Failure
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Vickrey Prices and Shortest Paths: What is an Edge Worth?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
An efficient and scalable approach to CNN queries in a road network
VLDB '05 Proceedings of the 31st international conference on Very large data bases
Efficient query processing on spatial networks
Proceedings of the 13th annual ACM international workshop on Geographic information systems
On the difficulty of some shortest path problems
ACM Transactions on Algorithms (TALG)
Query processing in spatial network databases
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Improved distance sensitivity oracles via random sampling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A near-linear time algorithm for computing replacement paths in planar directed graphs
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Oracles for Distances Avoiding a Failed Node or Link
SIAM Journal on Computing
Scalable network distance browsing in spatial databases
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Dual-failure distance and connectivity oracles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A nearly optimal oracle for avoiding failed vertices and edges
Proceedings of the forty-first annual ACM symposium on Theory of computing
Distance Oracles for Spatial Networks
ICDE '09 Proceedings of the 2009 IEEE International Conference on Data Engineering
Algorithm for computer control of a digital plotter
IBM Systems Journal
Path oracles for spatial networks
Proceedings of the VLDB Endowment
Replacement paths and k simple shortest paths in unweighted directed graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On trip planning queries in spatial databases
SSTD'05 Proceedings of the 9th international conference on Advances in Spatial and Temporal Databases
Finding the most vital arcs in a network
Operations Research Letters
Data centric research at the University of Queensland
ACM SIGMOD Record
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Shortest path query is one of the most fundamental queries in spatial network databases. There exist algorithms that can process shortest path queries in real time. However, many complex applications require more than just the calculation of a single shortest path. For example, one of the common ways to determine the importance (or price) of a vertex or an edge in spatial network is to use Vickrey pricing, which intuitively values the vertex v (or edge e) based on how much harder for travelling from the sources to the destinations without using v (or e). In such cases, the alternative shortest paths without using v (or e) are required. In this article, we propose using a precomputation based approach for both single pair alternative shortest path and all pairs shortest paths processing. To compute the alternative shortest path between a source and a destination efficiently, a naïive way is to precompute and store all alternative shortest paths between every pair of vertices avoiding every possible vertex (or edge), which requires O(n4) space. Currently, the state of the art approach for reducing the storage cost is to choose a subset of the vertices as center points, and only store the single-source alternative shortest paths from those center points. Such approach has the space complexity of O(n2 log n). We propose a storage scheme termed iSPQF, which utilizes shortest path quadtrees by observing the relationships between each avoiding vertex and its corresponding alternative shortest paths. We have reduced the space complexity from the naïive O(n4) (or the state of the art O(n4 log n)) to O(min(γ, L)n1.5) with comparable query performance of O(K), where K is the number of vertices in the returned paths, L is the diameter of the spatial network, and γ is a value that depends on the structure of the spatial network, which is empirically estimated to be 40 for real road networks. Experiments on real road networks have shown that the space cost of the proposed iSPQF is scalable, and both the algorithms based on iSPQF are efficient.