2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
I. Emiris , Div. of Comput. Sci., California Univ., Berkeley, CA, USA
J. Canny , Div. of Comput. Sci., California Univ., Berkeley, CA, USA
Algorithms modeled as algebraic branching programs, with inputs from an infinite ordered field, are studied. Direct perturbations on the input, so that an algorithm designed under the assumption of nondegeneracy can be applied to all inputs, are described. A deterministic method for algorithms with determinant tests and a randomized one for arbitrary test expressions are defined. They both incur extra complexity factors that are constant in several cases. Moreover, polynomial and exponential time algorithms always remain in the same complexity class while being enhanced with the power to execute on arbitrary inputs. Both methods are distinguished by their conceptual elegance and are significantly faster than previous ones.
complexity class, direct perturbations, polynomial time algorithms, degeneracies, algebraic branching programs, infinite ordered field, nondegeneracy, deterministic method, determinant tests, arbitrary test expressions, complexity factors, exponential time algorithms
I. Emiris, J. Canny, "A general approach to removing degeneracies", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 405-413, 1991, doi:10.1109/SFCS.1991.185399