TY - GEN
T1 - Randomly rounding rationals with cardinality constraints and derandomizations
AU - Doerr, Benjamin
PY - 2007/1/1
Y1 - 2007/1/1
N2 - We show how to generate randomized roundings of rational vectors that satisfy hard cardinality constraints and allow large deviations bounds. This improves and extends earlier results by Srinivasan (FOCS 2001), Gandhi et al. (FOCS 2002) and the author (STACS 2006). Roughly speaking, we show that also for rounding arbitrary rational vectors randomly or deterministically, it suffices to understand the problem for {0, 1/2} vectors (which typically is much easier). So far, this was only known for vectors with entries in 2 -ℓℤ, ℓ ∈ ℕ. To prove the general case, we exhibit a number of results of independent interest, in particular, a quite useful lemma on negatively correlated random variables, an extension of de Werra's (RAIRO 1971) coloring result for unimodular hypergraphs and a sufficient condition for a unimodular hypergraph to have a perfectly balanced non-trivial partial coloring. We also show a new solution for the general derandomization problem for rational matrices.
AB - We show how to generate randomized roundings of rational vectors that satisfy hard cardinality constraints and allow large deviations bounds. This improves and extends earlier results by Srinivasan (FOCS 2001), Gandhi et al. (FOCS 2002) and the author (STACS 2006). Roughly speaking, we show that also for rounding arbitrary rational vectors randomly or deterministically, it suffices to understand the problem for {0, 1/2} vectors (which typically is much easier). So far, this was only known for vectors with entries in 2 -ℓℤ, ℓ ∈ ℕ. To prove the general case, we exhibit a number of results of independent interest, in particular, a quite useful lemma on negatively correlated random variables, an extension of de Werra's (RAIRO 1971) coloring result for unimodular hypergraphs and a sufficient condition for a unimodular hypergraph to have a perfectly balanced non-trivial partial coloring. We also show a new solution for the general derandomization problem for rational matrices.
U2 - 10.1007/978-3-540-70918-3_38
DO - 10.1007/978-3-540-70918-3_38
M3 - Conference contribution
AN - SCOPUS:34547664809
SN - 9783540709176
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 441
EP - 452
BT - STACS 2007 - 24th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
PB - Springer Verlag
T2 - 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007
Y2 - 22 February 2007 through 24 February 2007
ER -