TY - GEN

T1 - Combinatorics and algorithms on low-discrepancy roundings of a real sequence

AU - Sadakane, Kunihiko

AU - Takki-Chebihi, Nadia

AU - Tokuyama, Takeshi

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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 effcient 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.

AB - 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 effcient 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.

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U2 - 10.1007/3-540-48224-5_14

DO - 10.1007/3-540-48224-5_14

M3 - Conference contribution

AN - SCOPUS:0037567799

SN - 3540422870

SN - 9783540422877

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 166

EP - 177

BT - Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings

A2 - Orejas, Fernando

A2 - Spirakis, Paul G.

A2 - van Leeuwen, Jan

PB - Springer Verlag

T2 - 28th International Colloquium on Automata, Languages and Programming, ICALP 2001

Y2 - 8 July 2001 through 12 July 2001

ER -