Abstract
The n-body simulation problem is stated as follows: Given initial positions and velocities of n particles that have pair-wise force interactions, simulate the movement of these particles so as to determine the positions of the particles at a future time.
In this paper, we give the first known n-body simulation algorithms with rigorous proofs of bounded error. The reachability problemis to determine if a specific particle will reach a certain region at some specified target time. In the case we require poly(n) bits of accuracy and where the target time is poly(n), our complexity bounds are surprisingly PSPACE.
We also have matching lower bounds for n-body simulation problem (in comparison all previous lower bound proofs required either artificial external forces or obstacles). We show that the reachability problem for a set of interacting particles in three dimensions is PSPACE-hard.
This research was supported by DARPA/ISTO Contracts N00014-88-K-0458, DARPA N00014-91-J-1985, N00014-91-C-0114, NASA subcontract 550-63 of prime contract NAS5-30428, US-Israel Binational NSF Grant 88-00282/2, and NSF Grant NSF-IRI-91-00681.
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© 1993 Springer-Verlag Berlin Heidelberg
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Reif, J.H., Tate, S.R. (1993). The complexity of N-body simulation. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_70
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DOI: https://doi.org/10.1007/3-540-56939-1_70
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