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Sweep Line

Sweep (or scanning) line algorithm is very efficient for some specific questions involving discrete intervals. The intervals could be the lasting time of events, or the width of a building or an abstract square, etc. In the scanning line algorithm, we usually need to distinguish the start and the end of an interval. After the labeling of the starts and ends, we can sort them together based on the values of the starts and ends.

Thus, if there are N intervals in total, we will have 2*N data points (since each interval will contribute 2). The sorting becomes the most time-consuming step, which is O(2N*log(2N) ~ O(N*logN). After the sorting, we usually can run a linear sweep for all the data points.

If the data point is labeled as a starting point, it means a new interval is in the processing; when an ending time is reached, it means one of the interval has ended. In such direct way, we can easily figure out how many intervals are in the processes. Other related information can also be obtained.

To sum up, the main features of the Sweep line algorithm

1. usually there are intervals involved;

2. the first step is to label the starts and the ends;

3. sort the data points from step 2;

4. do an O(N) sweep for all the data points.


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