Lower bounds for solving linear diophantine equations on random access machines
Journal of the ACM (JACM)
Simulating probabilistic by deterministic algebraic computation trees
Theoretical Computer Science
On the Optimality of Some Set Algorithms
Journal of the ACM (JACM)
On the complexity of unique solutions
Journal of the ACM (JACM)
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Are lower bounds easier over the reals?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Lower Bounds Are Not Easier over the Reals: Inside PH
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Circuits versus Trees in Algebraic Complexity
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Finding a vector orthogonal to roughly half a collection of vectors
Journal of Complexity
Decision versus evaluation in algebraic complexity
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Time complexity of decision trees
Transactions on Rough Sets III
An efficient algorithm for the sign condition problem in the semi-algebraic context
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Unimprovable Upper Bounds on Time Complexity of Decision Trees
Fundamenta Informaticae
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Let M be a parallel RAM with p processors and arithmetic operations addition and subtraction recognizing L ⊂ Nn in T steps. (Inputs for M are given integer by integer, not bit by bit.) Then L can be recognized by a (sequential) linear search algorithm (LSA) in O(n4(log(n) + T + log(p))) steps. Thus many n-dimensional restrictions of NP-complete problems (binary programming, traveling salesman problem, etc.) and even that of the uniquely optimum traveling salesman problem, which is &Dgr;P2-complete, can be solved in polynomial time by an LSA. This result generalizes the construction of a polynomial LSA for the n-dimensional restriction of the knapsack problem previously shown by the author, and destroys the hope of proving nonpolynomial lower bounds on LSAs for any problem that can be recognized by a PRAM as above with 2poly(n) processors in poly(n) time.