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
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Fast algorithms for N-dimensional restrictions of hard problems
Journal of the ACM (JACM)
On the complexity of functions for random access machines
Journal of the ACM (JACM)
How much can we speedup Gaussian elimination with pivoting?
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
A lower bound for randomized algebraic decision trees
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Randomized Ω(n2) lower bound for knapsack
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Randomized Complexity of Linear Arrangements and Polyhedra
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
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The problem of recognizing the language Ln(Ln, k) of solvable Diophantine linear equations with n variables (and solutions from {O, … , k}n) is considered. The languages ∪n&egr;N Ln, ∪n&egr;N Ln, l, the knapsack problem, are NP-complete. The &OHgr;(n2 lower bound for Ln,1 on linear search algorithms due to Dobkin and Lipton is generalized to an &OHgr;(n2log(k + 1)) lower bound for Ln, k. The method of Klein and Meyer auf der Heide is further improved to carry over the &OHgr;(n2) lower bound for Ln, 1 to random access machines (RAMS) in such a way that it holds for a large class of problems and for very small input sets. By this method, lower bounds that depend on the input size, as is necessary for Ln, are proved. Thereby, an &OHgr;(n2log(k + 1)) lower bound is obtained for RAMS recognizing Ln or Ln, k, for inputs from {0, … , (nk)0(n2)}n.