Fixed-dimensional parallel linear programming via relative {Epsilon}-approximations
We show that linear programming in IR{sup d} can be solved deterministically in O((log log n){sup d}) time using linear work in the PRAM model of computation, for any fixed constant d. Our method is developed for the CRCW variant of the PRAM parallel computation model, and can be easily implemented to run in O(log n(log log n){sup d-1}) time using linear work on an EREW PRAM. A key component in these algorithms is a new, efficient parallel method for constructing E-nets and E-approximations (which have wide applicability in computational geometry). In addition, we introduce a new deterministic set approximation for range spaces with finite VC-exponent, which we call the {delta}-relative {epsilon}-approximation, and we show how such approximations can be efficiently constructed in parallel.
- OSTI ID:
- 416794
- Report Number(s):
- CONF-960121--; CNN: Grant IRI-9116843; Grant CCR-9300079
- Country of Publication:
- United States
- Language:
- English
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