Combinatorics and algorithms for low-discrepancy, roundings of a real sequence

Authors:
Kunihiko Sadakane;Nadia Takki-Chebihi;Takeshi Tokuyama
Affiliations:
Department of Computer Science and Communication Engineering, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan and Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan;Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Venue:
Theoretical Computer Science - Automata, languages and programming
Year:
2005

Citing 9
Cited 0

Graph-Based Algorithms for Boolean Function Manipulation

IEEE Transactions on Computers
Digital halftones by dot diffusion

ACM Transactions on Graphics (TOG)
Faster scaling algorithms for network problems

SIAM Journal on Computing
Discrepancy theory

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
Matrix rounding under the Lp-discrepancy measure and its application to digital halftoning

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Fibonacci Cubes-A New Interconnection Topology

IEEE Transactions on Parallel and Distributed Systems
Optimal roundings of sequences and matrices

Nordic Journal of Computing
The structure and number of global roundings of a graph

COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We discuss the problem of computing all the integer sequences obtained by rounding an input sequence of n real numbers such that the discrepancy between the input sequence and each output binary sequence is less than one. The problem arises in the design of digital halftoning methods in computer graphics. We show that the number of such roundings is at most 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.