The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
A threshold of ln n for approximating set cover
Open accessAbstract
Given a collection ℱ of subsets of S = {1,…, n }, set cover is the problem of selecting as few as possible subsets from ℱ such that their union covers S, , and max k-cover is the problem of selecting k subsets from ℱ such that their union has maximum cardinality. Both these problems are NP-hard. We prove that (1 - o (1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low-order terms) between the ratio of approximation achievable by the greedy alogorithm (which is (1 - o (1)) ln n), and provious results of Lund and Yanakakis, that showed hardness of approximation within a ratio of (log 2 n ) / 2 ≃0.72 ln n . For max k -cover, we show an approximation threshold of (1 - 1/ e )(up to low-order terms), under assumption that P ≠ NP .
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Optimization, approximation, and complexity classes
Papadimitriou, C. H., & Yannakakis, M. (1991) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(91)90023-x · Cited by 1,653
Cited by
"Why Should I Trust You?": Explaining the Predictions of Any Classifier
Ribeiro, M. T., Singh, S., & Guestrin, C. (2016) · Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining · doi:10.1145/2939672.2939778 · Cited by 17,555
“Why Should I Trust You?”: Explaining the Predictions of Any Classifier
Ribeiro, M., Singh, S., & Guestrin, C. (2016) · Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Demonstrations · doi:10.18653/v1/n16-3020 · Cited by 6,682
Automatic subspace clustering of high dimensional data for data mining applications
Agrawal, R., Gehrke, J., Gunopulos, D., & Raghavan, P. (1998) · Proceedings of the 1998 ACM SIGMOD international conference on Management of data · doi:10.1145/276304.276314 · Cited by 2,412
Some optimal inapproximability results
Håstad, J. (2001) · Journal of the ACM · doi:10.1145/502090.502098 · Cited by 1,902
FastText.zip: Compressing text classification models
Joulin, A., Grave, E., Bojanowski, P., Douze, M., Jégou, H., & Mikolov, T. (2016) · arXiv · doi:10.48550/arxiv.1612.03651 · Cited by 887
Metadata
- Authors
- Feige, U.
- Venue
- Journal of the ACM
- Published
- 1998-07
- Volume
- 45
- Issue
- 4
- Pages
- 634-652
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2143996311
- Cited by
- 3,086
- References
- 1
- FWCI
- 41.68
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A threshold of ln n for approximating set cover. https://app.cochat.ai/papers/10.1145/285055.285059
- The paper
- Feige, U. (1998). A threshold of ln n for approximating set cover. Journal of the ACM. https://doi.org/10.1145/285055.285059
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
