相邻二次最短路的有效标号算法
Efficient labeling algorithms for adjacent quadratic shortest paths
摘要：
在这篇文章中，我们研究了相邻二次最短路问题（AQSPP），其中包括在寻找最短路径的有向图时，其总重量组件也包括连续弧的影响。我们提供了一个正式的描述AQSPP，并提出了一个扩展的Dijkstra的算法（我们表示aqD）解决AQSPP在多项式时间，并提供了一些温和的假设下证明其正确性。此外，我们引入了一个相邻的二次A* 算法（我们表示为aqA*）与向后搜索的成本去估计，以加快搜索。我们评估这两种算法的性能，通过比较它们的相对性能与基准算法从科学文献中，并进行了彻底收集的灵敏度分析的方法上的一组问题的特点，使用随机生成的图形。数值结果表明：（i）aqA* 优于所有其他算法，性能比aqD快约75倍，是最快的替代方案;（ii）当二次成本的大小变化时，所提出的解决方案过程不会失去效率;（iii）与科学文献中的基准算法相比，aqA* 和aqD在随机图实例上是最快的。我们得出结论的数值实验中提出的压力测试的AQSPP的背景下，真正的网格图的实例，大小高达$16 \times 10^6$节点，$64 \times 10^6$弧，和$10^9$二次弧。
英文摘要：
In this article, we study the Adjacent Quadratic Shortest Path Problem (AQSPP), which consists in finding the shortest path on a directed graph when its total weight component also includes the impact of consecutive arcs. We provide a formal description of the AQSPP and propose an extension of Dijkstra's algorithm (that we denote aqD) for solving AQSPPs in polynomial-time and provide a proof for its correctness under some mild assumptions. Furthermore, we introduce an adjacent quadratic A* algorithm (that we denote aqA*) with a backward search for cost-to-go estimation to speed up the search. We assess the performance of both algorithms by comparing their relative performance with benchmark algorithms from the scientific literature and carry out a thorough collection of sensitivity analysis of the methods on a set of problem characteristics using randomly generated graphs. Numerical results suggest that: (i) aqA* outperforms all other algorithms, with a performance being about 75 times faster than aqD and the fastest alternative; (ii) the proposed solution procedures do not lose efficiency when the magnitude of quadratic costs vary; (iii) aqA* and aqD are fastest on random graph instances, compared with benchmark algorithms from scientific literature. We conclude the numerical experiments by presenting a stress test of the AQSPP in the context of real grid graph instances, with sizes up to $16 \times 10^6$ nodes, $64 \times 10^6$ arcs, and $10^9$ quadratic arcs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
