Digital halftones by dot diffusion
ACM Transactions on Graphics (TOG)
Faster scaling algorithms for network problems
SIAM Journal on Computing
Handbook of combinatorics (vol. 2)
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Fibonacci Cubes-A New Interconnection Topology
IEEE Transactions on Parallel and Distributed Systems
On the Complexities of the Optimal Rounding Problems of Sequences and Matrices
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Generating randomized roundings with cardinality constraints and derandomizations
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Rounding of sequences and matrices, with applications
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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In this paper, we discuss the problem of computing all the integral sequences obtained by rounding an input real valued sequence such that the discrepancy between the input sequence and each output integral sequence is less than one. We show that the number of such roundings is n + 1 if we consider the discrepancy with respect to the set of all subintervals, and give an efficient algorithm to report all of them. Then, we give an optimal method to construct a compact graph to represent the set of global roundings satisfying a weaker discrepancy condition.