Theory of linear and integer programming
Theory of linear and integer programming
Selected papers of the 13th British Combinatorial Conference on British combinatorial conference
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Introduction to the Theory of Computation
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Theoretical Computer Science
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We study the hardness of the optimal jug measuring problem. By proving tight lower and upper bounds on the minimum number of measuring steps required, we reduce an inapproximable NP-hard problem (i.e., the shortest GCD multiplier problem [G. Havas, J.-P. Seifert, The Complexity of the Extended GCD Problem, in: LNCS, vol. 1672, Springer, 1999]) to it. It follows that the optimal jug measuring problem is NP-hard and so is the problem of approximating the minimum number of measuring steps within a constant factor. Along the way, we give a polynomial-time approximation algorithm with an exponential error based on the well-known LLL basis reduction algorithm.