The DOI matches its Crossref record; 159 of the 162 references it cites were found in a registry or an index.
Pseudo-Boolean optimization
Open accessOverview
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“The potentially large overhead in the number of variables lead to the development of several methods for degree reduction (e.g., References [160, 167, 168, 180, 188])”
From Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study (2024) · cites this paper as [168]
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 by Simulated Annealing
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983) · Science · doi:10.1126/science.220.4598.671 · Cited by 45,134
(1979) · Cited by 43,841
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
Theory of games and economic behavior
Garcia, S. R., & Miller, S. J. (2019) · American Mathematical Society eBooks · doi:10.1090/mbk/121/32 · Cited by 16,777
Reducibility among Combinatorial Problems
Karp, R. M. (1972) · Complexity of Computer Computations · doi:10.1007/978-1-4684-2001-2_9 · Cited by 11,511
Shapley, L. (1988) · Cambridge University Press eBooks · doi:10.1017/cbo9780511528446.003 · Cited by 10,698
17. A Value for n-Person Games
Shapley, L. S. (1953) · Contributions to the Theory of Games (AM-28), Volume II · doi:10.1515/9781400881970-018 · Cited by 6,950
Glover, F. (1990) · INFORMS journal on computing · doi:10.1287/ijoc.2.1.4 · Cited by 5,777
Glover, F. (1989) · INFORMS journal on computing · doi:10.1287/ijoc.1.3.190 · Cited by 5,469
The Theory of Games and Economic Behavior
Harrison, R. W., von Neumann, J., & Morgenstern, O. (1945) · Journal of Farm Economics · doi:10.2307/1232672 · Cited by 5,318
Research works printed but not linked: 17
- T. Badics, Approximation of some Nonlinear Binary Optimization Problems, Ph.D. Thesis, RUTCOR, Rutgers University, 1996.
- Balas, 1967, Extension de l'algorithme additif a la programmation en nombres at a la programmation non lineare, C. R. Acad. Sci. Paris, 258, 5136
- Banzhaf III, 1965, Weighted voting does not work: a mathematical analysis, Rutgers Law Rev., 19, 317
- Benzaken, 1983, Adjoints of pure bidirected graphs, Congr. Numer., 39, 123
- Fortet, 1959, L'algebre de Boole en recherche operationelle, Cahiers Études Centre Rech. Oper., 1, 5
- Fortet, 1960, Applications de l'algebre de Boole en recherche operationelle, Rev. Francaise Rech. Oper., 4, 17
- Hammer, 1968, Plant location—a pseudo-Boolean approach, Israel J. Technol., 6, 330
- Hammer, 1977, Pseudo-Boolean functions and game theory. I. Core elements and Shapley value, Cahiers Centre Etudes Rech. Oper., 19, 159
- Hammer, 1963, Application of discrete linear programming to the minimization of Boolean functions, Rev. Math. Pures Appl., 8, 459
- P. Hansen, B. Simeone, A class of quadratic pseudoboolean functions whose maximization is reducible to a network flow problem, CORR 79-39, Department of Comb. Optim., University of Waterloo.
- Laughhunn, 1971, Computational experience with capital expenditure programming models under risk, J. Business Finance, 3, 43
- Rosenberg, 1972, 0–1 optimization and non-linear programming, Rev. Française Automatique, Informatique Rech. Opér. (Série Bleue), 2, 95
- Rosenberg, 1975, Reduction of bivalent maximization to the quadratic case, Cahiers Centre Etudes Rech. Oper., 17, 71
- Rosenberg, 1980, Linear decompositions of positive real function of binary arguments, Utilitas Math., 17, 17
- I. Shepanik, Use of pseudo-boolean preference functions in metagame analysis, Ph.D. Thesis, Department of System Design, 1973.
- B. Simeone, Quadratic 0–1 programming, Boolean functions and graphs, Ph.D. Thesis in Combinatorics and Optimization, Waterloo, 1979.
- Trubin, 1969, On a method of solution of integer linear programming problems of special kind, Soviet Math. Dokl., 10, 1544
Cited by
Sorted by citations
Items 801–825 of 825
Monotone Boolean Reconstruction
Aslanyan, L. K., & Sahakyan, H. (2026) · Bolyai Society mathematical studies · doi:10.1007/978-3-032-18810-6_3
Backbone-Based Predict and Search for Pseudo-Boolean Optimization
Alvarado-Ulloa, B., Dilkina, B., Hochbaum, D. S., Ñanculef, R., & Asín‐Achá, R. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-27242-3_1
Han, S. I., Jeong, M., & Lee, Y. (2026) · Design, Automation, and Test in Europe · doi:10.23919/date69613.2026.11539684
Solving mixed-integer problems as QUBO: Encodings, reformulations, and rolling-precision algorithm
Iftakher, A., Türkay, M., & Hasan, M. M. F. (2026) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2026.109757
Intraspecific interactions facilitate mutualism across multilayer networks under weak selection
Ma, Y., Zhang, H., & Wang, C. (2026) · Journal of Mathematical Biology · doi:10.1007/s00285-026-02413-2
From Table Constraints to QUBO Models for Quantum Annealing
Codognet, P., & Monfroy, É. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-29918-5_1
The complete edge relaxation for binary polynomial optimization
Pia, A. D., & Khajavirad, A. (2026) · Mathematical Programming · doi:10.1007/s10107-026-02390-w
Li, X., Luo, S., Li, X., Wang, G., & Ding, G. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7038084
Semiring–based and valued CSPs revisited
Bistarelli, S., Fargier, H., Rossi, F., & Schiex, T. (2026) · Constraints · doi:10.1007/s10601-026-09388-3
Solving Branch Location Problem Using a Special Variant of VNS
Khabarov, M., Kochemazov, S., Otpuschennikov, I. V., & Semenov, A. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-31390-4_6
Александровна, Г. И., Kondratiev, V., & Semenov, A. (2026) · International Convention on Information and Communication Technology, Electronics and Microelectronics · doi:10.1109/mipro70003.2026.11591905
Evolutionary Tunneling and Periodicity Across the Big Valley Distribution
Whitley, D., Ochoa, G., & Chicano, F. (2026) · Genetic and Evolutionary Computation Conference (GECCO) · doi:10.1145/3795095.3805090
A reduction scheme for general-order Ising-like Hamiltonians in quantum heuristic solvers
Mao, C., Mosharev, P. A., Wang, Y., & Yung, M. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05339-2
Wang, Y., & Hahn, G. (2026) · Frontiers in Computer Science · doi:10.3389/fcomp.2026.1838774
Quantum Annealing Applications for Power Grid Modernization
Christeson, T. (2025) · Digital Commons - DU (University of Denver) · doi:10.56902/etdcrp.2025.223
Mochida, N., & Yasuda, S. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7330505
Dependence-aware design of typhoon-resilient offshore methanol platformsPreprint
Li, X., Luo, S., Li, X., Wang, G., & Ding, G. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7438751
High-efficiency wind farm layout optimization algorithm based on coherent Ising machine
Dai, B., Fan, Z. X., Fan, L., & Cao, C. (2026) · Laser Physics Letters · doi:10.1088/1612-202x/aea499
Lalwani, K., Sreedevi, V. V., Gakhar, M., Agrawal, D., & Tinker, D. (2026) · iScience · doi:10.1016/j.isci.2026.117726 · Cited by 1
HARDNESS OF RECONSTRUCTION FOR CLASSES OF MONOTONE BOOLEAN FUNCTIONS
Aslanyan, L. H., & Sahakyan, H. (2026) · Journal of Mathematical Sciences · doi:10.1007/s10958-026-08637-3
Research on QUBO Modeling Methods of COPs
Li, Y., Fan, C., Wang, X., Zhou, G., He, H., Lan, L., 黄奎华, & Cheng, J. (2026) · Learning and analytics in intelligent systems · doi:10.1007/978-3-032-26620-0_2
The Bipartite Implication Polytope: Conditional Relations over Multiple Sets of Binary Variables
Burlacu, R., Gemander, P., & Kuen, T. (2026) · SIAM Journal on Optimization · doi:10.1137/24m1655159
Minor Embedding for Max-Cut: Empirical Analysis of Quantum Annealing’s Combinatorial Bottleneck
Lavi, R., Moraglio, A., & Shir, O. M. (2026) · IEEE Congress on Evolutionary Computation · doi:10.1109/cec69861.2026.11727105
Object Segmentation and Markov Random Fields
Boykov, Y. Y. (2015) · Springer eBooks · doi:10.1007/978-0-387-09749-7_1
The Minimum Multicut Problem and an Exact Model for Cell Formation
Goldengorin, B. I., Krushinsky, D., & Pardalos, P. M. (2013) · Springer optimization and its applications · doi:10.1007/978-1-4614-8002-0_4
Metadata
- Authors
- Boros, E., & Hammer, P. L.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Corresponding author
- Boros, Endre
- Venue
- Discrete Applied Mathematics
- Publisher
- Elsevier BV
- Published
- 2002-11
- Volume
- 123
- Issue
- 1-3
- Pages
- 155-225
- ISSN
- 0166-218X (ISSN-L)
- OpenAlex
- W2074078071
- Cited by
- 827
- References
- 162
- Citations by year
- 2026: 34 · 2025: 34 · 2024: 27 · 2023: 33 · 2022: 32 · 2021: 28 · 2020: 35 · 2019: 39 · 2018: 42 · 2017: 38 · 2016: 35 · 2015: 43 · 2014: 62 · 2013: 58 · 2012: 52
- FWCI
- 9.97
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Discrete Applied Mathematics (publishedVersion)
- Rutgers University Community Repository (Rutgers University) (submittedVersion)
- ORBi (University of Liège) (submittedVersion, other-oa)
- Funders
- National Science Foundation (9806389)
- Office of Naval Research (N00014-92-J-1375, N00014)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Graph Theory Research
- Keywords
- pseudo-Boolean optimization, set functions, algebraic expressions, approximation algorithms, combinatorial optimization
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