如何在道路網中兩點之間移動時，找到快速移動路徑在長久以來已經有很多研究。但這些直接找到兩點之間移動的快速移動路徑，並沒有辦法讓使用者，在他們前往目的地時依照某些目的或是偏好，考量所花費的時間，而選擇出所必須要經過的中繼點。並沒有辦法讓使用者對於他們在前往目的地時，為了某些目的而想要依照各種適合的花費時間來選擇出他們必須經過的中繼點。

像是平常要開車去餐廳或開會，常常會需要選擇停車場，然後開車到停車場停車，接著再走路到餐廳或會議中心，這就會有不同的偏好來考慮這兩種花費的時間。更因為交通狀況會隨著時間改變，所以隨著不同出發時間，也使的剛剛所提的兩種花費時間不斷的變化，這使得使用者更加難以判斷來做出選擇。所以我們針對這樣的問題提出中繼點快速路徑之推薦。讓使用者滿足各種不同的目的或偏好，而考慮有利的花費時間，提供出這些中繼點來選擇。

我們提出兩種最低花費時間的評估方式，以降低在處理中繼點快速路徑之推薦時，所必須花費大量的計算及搜尋空間。透由一系列的實驗驗證這兩種評估最低花費時間的方式。

How to efficiently find the fastest path between two given positions is an important topic in road networks. However, previous works can’t help users to choose the path that must across certain kinds of intermediate positions by considering heterogeneous travel costs. For example, the user may need a parking lot on the way to the restaurant, and both of the driving time and walk time are concerned. In addition, the traffic conditions often vary as time goes by. A chosen departure time for the travel can significantly reduce the related travel costs. These real requirements motivate us to study the issue of fast paths recommendation, which list all the advantageous intermediate positions and the corresponding paths for the user to select. In this paper, we propose a novel approach to solve this problem by applying the extended skyline techniques on all possible time sub-intervals for the final answers. For better performance, two bounds in road networks, i.e., the travel time lower bound and the travel time lower bound in time interval are introduced. We use the travel time lower bound to prune useless intermediate nodes by using a maximal speed in road network to restrict the search space. Then, the travel time lower bound in time interval is adopted to reduce computation of the fast paths for intermediate nodes by using a lower maximal speed in a time interval to diminish the search time. A series of experiments are performed to demonstrate that the proposed approaches based on the two bounds are more effective and efficient than the straightforward method for the fast paths recommendation.

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