The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Minimizing a Submodular Function on a Lattice
Abstract
This paper gives general conditions under which a collection of optimization problems, with the objective function and the constraint set depending on a parameter, has optimal solutions that are an isotone function of the parameter. Relating to this, we present a theory that explores and elaborates on the problem of minimizing a submodular function on a lattice.
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
Foundations of Economic Analysis.
Stigler, G. J., & Samuelson, P. A. (1948) · Journal of the American Statistical Association · doi:10.2307/2280713 · Cited by 4,128
Ford, D. R., & Fulkerson, D. R. (1962) · Cited by 4,072
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV
Roy, H. L. L., Lecam, L., & Neyman, J. (1969) · Revue de l'Institut International de Statistique / Review of the International Statistical Institute · doi:10.2307/1402306 · Cited by 2,835
A lattice-theoretical fixpoint theorem and its applications
Tarski, A. (1955) · Pacific Journal of Mathematics · doi:10.2140/pjm.1955.5.285 · Cited by 2,704
Dynamic Version of the Economic Lot Size Model
Wagner, H. M., & Whitin, T. M. (2004) · Management Science · doi:10.1287/mnsc.1040.0262 · Cited by 2,056
Ore, Ö. (1962) · Medical Entomology and Zoology · Cited by 1,529
Linear Programming Under Uncertainty
Dantzig, G. B. (2004) · Management Science · doi:10.1287/mnsc.1040.0261 · Cited by 1,173
Dynamic Inventory Policy with Varying Stochastic Demands
Karlin, S. (1960) · Management Science · doi:10.1287/mnsc.6.3.231 · Cited by 302
Complements and substitutes in the opttmal assignment problem
Shapley, L. S. (1962) · Naval Research Logistics Quarterly · doi:10.1002/nav.3800090106 · Cited by 122
Cited by
Comparative Economic Organization: The Analysis of Discrete Structural Alternatives
Williamson, O. E. (1991) · Administrative Science Quarterly · doi:10.2307/2393356 · Cited by 7,151
Towards a theory of ecosystems
Jacobides, M. G., Cennamo, C., & Gawer, A. (2018) · Strategic Management Journal · doi:10.1002/smj.2904 · Cited by 3,724
Putting Auction Theory to Work
Milgrom, P. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511813825 · Cited by 1,642
Levina, N., & Ross, J. W. (2003) · MIS Quarterly · doi:10.2307/30036537 · Cited by 699
Selling to Overconfident Consumers
Grubb, M. D. (2009) · American Economic Review · doi:10.1257/aer.99.5.1770 · Cited by 316
Metadata
- Authors
- Topkis, D. M.
- Venue
- Operations Research
- Published
- 1978-04
- Volume
- 26
- Issue
- 2
- Pages
- 305-321
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W2161413792
- Cited by
- 1,315
- References
- 9
- FWCI
- 10.52
- Type
- journal article
- Language
- en
- Open access
- closed
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: Minimizing a Submodular Function on a Lattice. https://app.cochat.ai/papers/10.1287/opre.26.2.305
- The paper
- Topkis, D. M. (1978). Minimizing a Submodular Function on a Lattice. Operations Research. https://doi.org/10.1287/opre.26.2.305
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.
