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 (\(k\text {SPwLO}\)) 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 \(k\text {SPwLO}\) 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.

中文翻译：

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查找k个最短路径且重叠有限

在本文中，我们研究了道路网络中两个位置之间的替代路径的计算。更具体地说，我们研究了具有有限重叠（\（k \ text {SPwLO} \））的k个最短路径，该问题旨在找到一组k条路径，以使所有路径彼此足够不同并且尽可能短。为了计算\（k \ text {SPwLO} \）查询，我们提出了两种精确的算法，称为OnePass和MultiPass，我们正式证明了MultiPass就复杂性而言是最佳的。我们还研究了两类启发式算法：（a）面向性能的启发式算法，它以性能为代价换取了简短性，即，它们减少了查询处理时间，但不保证每个后续结果的长度都是最小的；（b）面向完整性的启发式算法，将不相似性换为完整性，即，它们放宽了相似性约束以返回包含正好包含k条路径的结果。在真实道路网络上进行的广泛实验分析证明了我们提出的解决方案在运行时间和结果质量方面的效率。