地图提供商(如谷歌或Yahoo!地图)指示方向?

I mean, they probably have real-world data in some form, certainly including distances but also perhaps things like driving speeds, presence of sidewalks, train schedules, etc. But suppose the data were in a simpler format, say a very large directed graph with edge weights reflecting distances. I want to be able to quickly compute directions from one arbitrary point to another. Sometimes these points will be close together (within one city) while sometimes they will be far apart (cross-country).

Graph algorithms like Dijkstra's algorithm will not work because the graph is enormous. Luckily, heuristic algorithms like A* will probably work. However, our data is very structured, and perhaps some kind of tiered approach might work? (For example, store precomputed directions between certain "key" points far apart, as well as some local directions. Then directions for two far-away points will involve local directions to a key points, global directions to another key point, and then local directions again.)

实践中实际使用的算法是什么?

PS:这个问题的动机是发现在线地图方向的怪癖。与三角形不等式相反,有时谷歌Maps认为X-Z比使用中间点(如X-Y-Z)花费的时间更长,距离更远。但也许他们的行走方向也会优化另一个参数?

pp。这是对三角不等式的另一个违反,这表明(对我来说)他们使用了某种分层方法:X-Z vs X-Y-Z。前者似乎使用了著名的塞瓦斯托波尔大道(Boulevard de Sebastopol),尽管它有点偏僻。

编辑:这两个例子似乎都不起作用了,但在最初的帖子发布时都起作用了。


当前回答

Probably similar to the answer on pre-computed routes between major locations and layered maps, but my understanding is that in games, to speed up A*, you have a map that is very coarse for macro navigation, and a fine-grained map for navigation to the boundary of macro directions. So you have 2 small paths to calculate, and hence your search space is much much smaller than simply doing a single path to the destination. And if you're in the business of doing this a lot, you'd have a lot of that data pre-computed so at least part of the search is a search for pre-computed data, rather than a search for a path.

其他回答

事实上,我已经做过很多次了,尝试了几种不同的方法。根据地图的大小(地理位置),您可能会考虑使用haversine函数作为启发式方法。

我的最佳解决方案是使用带有直线距离的A*作为启发式函数。但接下来你需要地图上每个点(交集或顶点)的某种坐标。您还可以为启发式函数尝试不同的权重,即。

f(n) = k*h(n) + g(n)

k是一个大于0的常数。

我有点惊讶这里没有提到Floyd Warshall的算法。这个算法很像Dijkstra算法。它还有一个很好的特性,那就是它允许你计算,只要你想继续允许更多的中间顶点。因此,它自然会很快找到使用州际公路或高速公路的路线。

以下是世界上最快的路由算法的比较和正确性:

http://algo2.iti.uka.de/schultes/hwy/schultes_diss.pdf

下面是谷歌关于这个主题的技术演讲:

http://www.youtube.com/watch?v=-0ErpE8tQbw

以下是schultes所讨论的高速公路层次算法的实现(目前仅在柏林,我正在编写界面,移动版本也正在开发中):

http://tom.mapsforge.org/

我知道OP里的地图是怎么回事了:

用指定的中间点来观察路线:由于那条路不直,这条路线略微向后走。

如果他们的算法不会回溯,它就看不到更短的路线。

I was very curious about the heuristics used, when a while back we got routes from the same starting location near Santa Rosa, to two different campgrounds in Yosemite National Park. These different destinations produced quite different routes (via I-580 or CA-12) despite the fact that both routes converged for the last 100 miles (along CA-120) before diverging again by a few miles at the end. This was quite repeatable. The two routes were up to 50 miles apart for around 100 miles, but the distances/times were pretty close to each other as you would expect.

唉,我无法重现——算法肯定已经改变了。但这让我对算法很好奇。我所能推测的是,有一些方向修剪,恰好对从远处看的目的地之间的微小角度差异非常敏感,或者有不同的最终目的地选择的预先计算的片段。