Abstract
We provide the first hardness result for the Covering Radius Problem on lattices (CRP). Namely, we show that for any large enough p ≤ ∞ there exists a constant cp > 1 such that CRP in the ℓp norm is ∏2-hard to approximate to within any constant less than c p. In particular, for the case p = ∞, we obtain the constant c∞ = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be ∏2-hard. As part of our proof, we establish a stronger hardness of approximation result for the ∀∃-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006 |
| Pages | 145-158 |
| Number of pages | 14 |
| Volume | 2006 |
| DOIs | |
| State | Published - 2006 |
| Event | 21st Annual IEEE Conference on Computational Complexity, CCC 2006 - Prague, Czech Republic Duration: Jul 16 2006 → Jul 20 2006 |
Other
| Other | 21st Annual IEEE Conference on Computational Complexity, CCC 2006 |
|---|---|
| Country | Czech Republic |
| City | Prague |
| Period | 7/16/06 → 7/20/06 |
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ASJC Scopus subject areas
- Computational Mathematics
Cite this
Hardness of the covering radius problem on lattices. / Haviv, Ishay; Regev, Oded.
Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. Vol. 2006 2006. p. 145-158 1663733.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Hardness of the covering radius problem on lattices
AU - Haviv, Ishay
AU - Regev, Oded
PY - 2006
Y1 - 2006
N2 - We provide the first hardness result for the Covering Radius Problem on lattices (CRP). Namely, we show that for any large enough p ≤ ∞ there exists a constant cp > 1 such that CRP in the ℓp norm is ∏2-hard to approximate to within any constant less than c p. In particular, for the case p = ∞, we obtain the constant c∞ = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be ∏2-hard. As part of our proof, we establish a stronger hardness of approximation result for the ∀∃-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere.
AB - We provide the first hardness result for the Covering Radius Problem on lattices (CRP). Namely, we show that for any large enough p ≤ ∞ there exists a constant cp > 1 such that CRP in the ℓp norm is ∏2-hard to approximate to within any constant less than c p. In particular, for the case p = ∞, we obtain the constant c∞ = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be ∏2-hard. As part of our proof, we establish a stronger hardness of approximation result for the ∀∃-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere.
UR - http://www.scopus.com/inward/record.url?scp=34247486199&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34247486199&partnerID=8YFLogxK
U2 - 10.1109/CCC.2006.23
DO - 10.1109/CCC.2006.23
M3 - Conference contribution
AN - SCOPUS:34247486199
SN - 0769525962
SN - 9780769525969
VL - 2006
SP - 145
EP - 158
BT - Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006
ER -