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Lower bounds for cutting planes proofs with small coefficients
1995
Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
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Acknowledgements The authors would like to thank Russell Impagliazzo, Jan Krajicek and Sam Buss for very helpful conversations. ...
in small-weights
Cutting
Planes. ...
In Section 4, we will prove lower bounds for both of the above generalizations of Cutting Planes. ...
doi:10.1145/225058.225275
dblp:conf/stoc/BonetPR95
fatcat:zqdlacylzvcxpiq4yw7w77j4r4
The Space Complexity of Cutting Planes Refutations
2015
Computational Complexity Conference
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cutting planes proofs of the pigeonhole principle with coefficients bounded by two. ...
This is in contrast to the weaker resolution proof system, for which the analogous space measure has been well-studied and many optimal lower bounds are known. ...
Results for cutting planes with small coefficients The constant space refutations in Theorem 5 use coefficients as big as 2 n , and these seem to be necessary for our proof technique to work. ...
doi:10.4230/lipics.ccc.2015.433
dblp:conf/coco/GalesiPT15
fatcat:n736vrqq25d5pkys57umbmhpj4
Semantic Versus Syntactic Cutting Planes
2016
Symposium on Theoretical Aspects of Computer Science
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First, we show that the lower bound technique of [22] applies also to semantic cutting planes: the proof system has feasible interpolation via monotone real circuits, which gives an exponential lower bound ...
In particular, we give a formula for which any refutation in syntactic cutting planes requires exponential length, while there is a polynomial length refutation in semantic cutting planes. ...
A lower bound for cutting planes with small coefficients was obtained by [4] and [18] , and [14] gave a lower bound for the tree-like version of the system. ...
doi:10.4230/lipics.stacs.2016.35
dblp:conf/stacs/FilmusHL16
fatcat:pp6k6laesfapjnpbqzx6g3p2oe
Stabbing Planes
[article]
2022
arXiv
pre-print
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Finally, we prove linear lower bounds on the rank of Stabbing Planes refutations by adapting lower bounds in communication complexity and use these bounds in order to show that Stabbing Planes proofs cannot ...
We develop a new semi-algebraic proof system called Stabbing Planes which formalizes modern branch-and-cut algorithms for integer programming and is in the style of DPLL-based modern SAT solvers. ...
This allowed them to lift the exponential lower bounds on Cutting Planes proofs [36, 39, 48, 67] to SP * , and even to SP proofs with coefficients of size exp(n δ ) for some constant δ < 1. ...
arXiv:1710.03219v2
fatcat:4dedtl7iordyvcmquixcpwmd6y
On the Power and Limitations of Branch and Cut
[article]
2021
arXiv
pre-print
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First, we show that any Stabbing Planes proof with bounded coefficients SP* can be translated into Cutting Planes. ...
As a consequence of the known lower bounds for Cutting Planes, this establishes the first exponential lower bounds on SP*. ...
Our second lower bound is a new linear depth lower bound for semantic Cutting Planes proofs. ...
arXiv:2102.05019v2
fatcat:2kls6apafjbzxlsw2pfpkyissm
A Rank Lower Bound for Cutting Planes Proofs of Ramsey's Theorem
2016
ACM Transactions on Computation Theory
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In particular we focus on the propositional proof system cutting planes; we prove that the upper bound "r(k, k) ≤ 4 k " requires cutting planes proof of high rank. ...
We study the complexity of proving upper bounds for the number r(k, k). ...
Lower bounds for more natural formulas exist for cutting plane proofs of restricted forms (e.g. when the numeric coefficients are small [6] or the proof is tree-like [19] ). ...
doi:10.1145/2903266
fatcat:aikdisyslzflboe65jqgi6p4l4
A finitely converging cutting plane technique
1985
Operations Research Letters
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The primary 'theoretical' contribution is the simplicity of the proof of convergence. programming * integer * cutting planes ...
We consider a new finitely convergent cutting plane algorithm for mixed integer linear programs in which the optimal objective value is assumed to be integral. ...
Acknowledgement I wish to thank David Bell for his helpful comments on an earlier version of this note. ...
doi:10.1016/0167-6377(85)90041-0
fatcat:boo5hptlbzdkxdhcxwq3qc5ola
Page 7539 of Mathematical Reviews Vol. , Issue 98M
[page]
1998
Mathematical Reviews
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Summary: “We consider small-weight cutting planes (CP" ) proofs; that is, cutting planes (CP) proofs with coefficients up to Poly(n). ...
proofs with small coefficients. ...
Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity
[article]
2020
arXiv
pre-print
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We apply our generalized theorem to solve two open problems: * We present the first result that demonstrates a separation in proof power for cutting planes with unbounded versus polynomially bounded coefficients ...
Specifically, we exhibit CNF formulas that can be refuted in quadratic length and constant line space in cutting planes with unbounded coefficients, but for which there are no refutations in subexponential ...
Part of this work was carried out while several of the authors were visiting the Simons Institute for the Theory of Computing in association with the DIMACS/Simons Collaboration on Lower Bounds in Computational ...
arXiv:2001.02144v1
fatcat:urgi4cd5vvczdnsqcnqloxsj6q
Cuts from proofs: a complete and practical technique for solving linear inequalities over integers
2011
Formal methods in system design
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Our main insight is that by focusing on the defining constraints of a vertex, we can compute a proof of unsatisfiability for the intersection of the defining constraints and use this proof to systematically ...
exclude subspaces of the feasible region with no integer points. ...
We would also like to thank David Dill for his useful suggestions and Suhabe Bugrara for his comments on a draft of this paper. ...
doi:10.1007/s10703-011-0127-z
fatcat:4y5meofrvfe67l7vaatv4oa7yy
Cuts from Proofs: A Complete and Practical Technique for Solving Linear Inequalities over Integers
[chapter]
2009
Lecture Notes in Computer Science
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Our main insight is that by focusing on the defining constraints of a vertex, we can compute a proof of unsatisfiability for the intersection of the defining constraints and use this proof to systematically ...
exclude subspaces of the feasible region with no integer points. ...
We would also like to thank David Dill for his useful suggestions and Suhabe Bugrara for his comments on a draft of this paper. ...
doi:10.1007/978-3-642-02658-4_20
fatcat:yn6f3645ijbihpdqqahps5u6ie
A Rank Lower Bound for Cutting Planes Proofs of Ramsey's Theorem
[chapter]
2013
Lecture Notes in Computer Science
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In particular we focus on the propositional proof system cutting planes; we prove that the upper bound "r(k, k) ≤ 4 k " requires cutting planes proof of high rank. ...
We study the complexity of proving upper bounds for the number r(k, k). ...
We are now ready to prove the lower bound on rank of cutting planes proof of the Ramsey number upper bound. Theorem 7. For all even k ≥ 4, cutting planes rank of formula Ram k is at least 2 k/2−1 . ...
doi:10.1007/978-3-642-39071-5_26
fatcat:tb624rsot5dtbi56vwgstndnku
Optimized Risk Scores
2017
Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '17
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We formulate the risk score problem as a mixed integer nonlinear program, and present a cutting plane algorithm to recover its optimal solution. ...
These models are widely used in medicine and criminal justice, but are difficult to learn from data because they need to be calibrated, sparse, use small integer coefficients, and obey application-specific ...
We would like to thank Paul Rubin for helpful discussions. We would also like to thank our collaborators Aaron Struck and Brandon Westover for their guidance on the seizure prediction application. ...
doi:10.1145/3097983.3098161
dblp:conf/kdd/UstunR17
fatcat:vcfyutt3jfa2lfbagzdeakhsbu
Depth lower bounds in Stabbing Planes for combinatorial principles
[article]
2021
arXiv
pre-print
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The techniques known so far to prove size and depth lower bounds for Stabbing Planes are generalizations of those used for the Cutting Planes proof system established via communication complexity arguments ...
By the covering method we obtain a superlinear size lower bound and a logarithmic depth lower bound for Stabbing Planes proof of Tseitin contradictions over a grid graph. ...
In this paper we further develop the study of proof depth for SP. Rank lower bound techniques for Cutting Planes are essentially of two types. ...
arXiv:2102.07622v2
fatcat:gjrnams6ynhf3kjj7ih67uegam
Bounds on the size of branch-and-bound proofs for integer knapsacks
2008
Operations Research Letters
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Using a direct counting argument, we derive lower and upper bounds for the number of nodes enumerated by linear programming-based branch-and-bound (B&B) method to prove the infeasibility of an integer ...
Acknowledgments The author would like to thank Gábor Pataki from the University of North Carolina at Chapel Hill for having constructive discussions and providing helpful suggestions on the material presented ...
Most commercial solvers use cutting planes in conjunction with B&B (termed branch-and-cut methods). ...
doi:10.1016/j.orl.2007.04.011
fatcat:dzcckx3lxfetvoxbpbqf3hm6ey
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