Skyline: the needle in the haystack
Impossible to find a point which is at least as good in every criteria
Suppose you intend to travel for vacation and you are undecided about the hotel to patronize. Of course, you would like a hotel that is affordable with good customer ratings and close to the city centre, you may even want one with large rooms.
However, keep in mind you can’t have it all. A cheap hotel may not have an excellent rating, if it does, it might be farther than the city centre or have small rooms. Some hotels may be cheaper and bigger than others however for some the distinctions aren’t clear. The best set of hotels which is incomparable with each other is called a skyline. In economics, we call this the Pareto-optimal point where no individual or preference criterion can be better off without making at least one individual or preference criterion worse off or without any loss thereof. In other words, for any point in the skyline, it is impossible to find a point that is at least as good in every regard.
I collected data from Kaggle about 120 hotel rooms in Bosnia (link to data) which includes their characteristics such as size (square feet), price, ratings, etc as shown below.
Suppose you are looking for a hotel you might to find one that is cheap, big, and close to the city centre. Instead of looking at each hotel you could first compute the skyline and check those instead.
Assuming I’m interested in the following qualities in a hotel:
Low price, close to the city centre (low distance), big room (size square metre), and good customer ratings.
There are 31 hotel rooms in the skyline coloured in orange.
2. Low price, close to the city centre (low distance) and big rooms (square metre). There are 10 hotel rooms in the skyline (coloured in yellow).
3. Lower price and higher customer ratings. There are 4 hotel rooms in the skyline (coloured in red).
Depending on your interest, before checking all the hotel rooms it is advisable to first look at the hotel rooms in the skyline.
Applications
The concept of skylines can be implemented by travel agencies to rank flight and hotel deals when recommending deals to users.
Companies can use it to detect high achieving employees receiving low salaries.
Reference
Max Halford: skyline queries on python
Hotels data: Kaggle bosnia hotel data