论文标题
探测一组轨迹以最大化捕获的信息
Probing a Set of Trajectories to Maximize Captured Information
论文作者
论文摘要
我们研究了一个轨迹分析问题，我们称之为轨迹捕获问题（TCP），其中，对于给定的输入集$ {\ cal t} $，飞机上的轨迹的$ {\ cal t} $，以及一个整数$ k \ geq 2 $，我们试图计算$ k $的集合（``Portals''的$ k $ points $ knital poster的总poster $ subtra $ subtra $ subtra fors partra faster a subtra fars of subtra a caltra faster的库。这个问题自然出现在轨迹分析和摘要中。 我们表明，TCP是NP-HARD（即使在非常特殊的情况下），并给出一些第一个近似结果。我们的主要重点是采用实用算法工程方法攻击TCP，包括整数线性编程（以解决实例以证明最优性）和本地搜索方法。我们研究了这种方法产生的完整性差距。我们分析了不同类别数据的方法，包括我们生成的基准实例。我们的目标是根据解决方案时间和解决方案质量了解最佳性能的启发式方法。我们证明我们能够为现实世界实例计算可证明的最佳解决方案。
We study a trajectory analysis problem we call the Trajectory Capture Problem (TCP), in which, for a given input set ${\cal T}$ of trajectories in the plane, and an integer $k\geq 2$, we seek to compute a set of $k$ points (``portals'') to maximize the total weight of all subtrajectories of ${\cal T}$ between pairs of portals. This problem naturally arises in trajectory analysis and summarization. We show that the TCP is NP-hard (even in very special cases) and give some first approximation results. Our main focus is on attacking the TCP with practical algorithm-engineering approaches, including integer linear programming (to solve instances to provable optimality) and local search methods. We study the integrality gap arising from such approaches. We analyze our methods on different classes of data, including benchmark instances that we generate. Our goal is to understand the best performing heuristics, based on both solution time and solution quality. We demonstrate that we are able to compute provably optimal solutions for real-world instances.
