Abstract
In this paper, we investigate the computation of alternative paths between two locations in a road network. More specifically, we study the k-shortest paths with limited overlap (ktext {SPwLO}) problem that aims at finding a set of k paths such that all paths are sufficiently dissimilar to each other and as short as possible. To compute ktext {SPwLO} queries, we propose two exact algorithms, termed OnePass and MultiPass, and we formally prove that MultiPass is optimal in terms of complexity. We also study two classes of heuristic algorithms: (a) performance-oriented heuristic algorithms that trade shortness for performance, i.e., they reduce query processing time, but do not guarantee that the length of each subsequent result is minimum; and (b) completeness-oriented heuristic algorithms that trade dissimilarity for completeness, i.e., they relax the similarity constraint to return a result that contains exactly k paths. An extensive experimental analysis on real road networks demonstrates the efficiency of our proposed solutions in terms of runtime and quality of the result.
Highlights
Computing the shortest path between two locations in a road network is a fundamental problem that has attracted lots of attention by both the research community and industry
We prove that the k-shortest paths with limited overlap (kSPwLO) problem is weakly N P-hard, and we propose two exact algorithms that traverse the road network by expanding paths from the source in length order, while employing pruning criteria to reduce the number of paths that need to be examined
While various measures to compute the similarity between two paths have been proposed [22], we argue that the similarity measure of Eq 1 is the most suitable one for alternative routing on road networks, as it enables us to disregard needlessly long paths when searching for alternative paths
Summary
Computing the shortest path between two locations in a road network is a fundamental problem that has attracted lots of attention by both the research community and industry. This paper extends our previous work [9,10] where we presented the following contributions: Fig. 1 Motivating example a set of dissimilar paths [18] or by employing edge penalties [3] These methods provide no formal definition of the alternative routing problem, and typically no guarantee regarding the length of the recommended paths. – We presented three performance-oriented heuristic algorithms that limit the number of examined paths but do not minimize the length of each subsequent result: OnePass+ employs the pruning power of MultiPass but traverses the network only once; SVP+ selects alternative paths from the set of single-via paths [2]; ESX removes edges from the road network incrementally and computes the shortest path on the updated network Through an extensive experimental analysis on real road networks, we evaluate both the algorithms presented in our previous works and the new ones in terms of runtime, quality of alternative paths and completeness of the result set (Sect. 9)
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