Table 2
Algorithmic efficiency.
| Algorithmic step | Runtime ∝ O(·) | Memory ∝ O(·) |
|---|---|---|
| Create particle list | N | N |
| Sort particle list | NlogN | 1 |
| Create collision list | N2є |  |
| Sort collision list |  |
1 |
| Reduce particle list | log N | 0 |
| Ereate κ fragments | κ | κ |
| Sort κ fragments | κ log κ | 1 |
| Merge particle lists | N + κ | 1 |
| Reduce collision list |  |
0 |
| Create new collision list | κN |  |
| Merge collision lists |  |
1 |
| Total simulation |  |
 |
Notes. Order estimations, in big O, of the time and memory requirement in Keplerian collision detection. The top shows the initialisation, the middle rows show the managing of one collision, and the bottom is for the full simulation. This total is found because there are an expected O(N2s2/Ia2) collisions in any fixed simulation time. For comparison, the time complexity for tree codes scales as O(N4/3I−1/3log N). The parameter κ is the number of fragments produced in a collision.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.