|
The characteristic structure of N-body problem is an observable that depends on all pairs of entities from a set of N entities.
|
|
This structure is seen in diverse applications:
|
|
1)Look at a database of items and calculate some form of correlation between all pairs of database entries
|
|
2)This was first used in studies of measurements of a "chaotic dynamical system" with points xi which are vectors of length m
|
|
Put rij = distance between xi and xj in m dimensional space
|
Then probability p(rij = r) is proportional to r(d-1)
-
where d (not equal to m) is dynamical dimension of system
-
calculate by forming all the rij (for i and j running over observable points from our system -- usually a time series) and accumulating in a histogram of bins in r
-
Parallel algorithm in a nutshell: Store histograms replicated in all processors, distribute vectors equally in each processor and just pipeline xj through processors and as they pass through accumulate rij ; add histograms together at end.
|
