### Citations

347 | Cones of matrices and set-functions and 0− 1 optimization,
- Lovasz, Schrijver
- 1991
(Show Context)
Citation Context ...P-based proof systems are Cutting Planes (introduced as a general method for solving ILP in [3], and as a proof system in [2]) and Lovász-Schrijver (introduced as a general method for solving ILP in =-=[6]-=-, and first considered as a proof system in [8]). A number of mixtures of ILP-based proof systems and algebraic proof systems are introduced and studied in [4]. Another method for solving ILP was prop... |

295 |
An algorithm for integer solutions to linear programs,"
- Gomory
- 1963
(Show Context)
Citation Context ...al proof systems based on different methods for solving Integer Linear Programming The two most important ILP-based proof systems are Cutting Planes (introduced as a general method for solving ILP in =-=[3]-=-, and as a proof system in [2]) and Lovász-Schrijver (introduced as a general method for solving ILP in [6], and first considered as a proof system in [8]). A number of mixtures of ILP-based proof sy... |

252 |
A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems,
- Sherali, Adams
- 1990
(Show Context)
Citation Context ...roof system in [8]). A number of mixtures of ILP-based proof systems and algebraic proof systems are introduced and studied in [4]. Another method for solving ILP was proposed by Sherali and Adams in =-=[11]-=- but has not been explored as a propositional proof system up to now. The SA relaxation is interesting in that it is static and is stronger than LS, the Lovász-Schrijver relaxation without semidefini... |

121 | A comparison of the Sherali-Adams, Lovasz-Schrijver and Lasserre relaxations for 0-1 programming.
- Laurent
- 2003
(Show Context)
Citation Context ...onal proof system up to now. The SA relaxation is interesting in that it is static and is stronger than LS, the Lovász-Schrijver relaxation without semidefinite cuts. More precisely, it is proven in =-=[5]-=- that rank k SA relaxation is tighter than rank k LS relaxation. A number of lower bounds have been proven for the ILPbased proof systems. A non-comprehensive list of Previous results relevant to our ... |

41 | Rank bounds and integrality gaps for cutting planes procedures
- Buresh-Oppenheim, Galesi, et al.
- 2003
(Show Context)
Citation Context ...s have been proven for the ILPbased proof systems. A non-comprehensive list of Previous results relevant to our work include the LS and LS+ rank lower bounds for a number of specific tautologies from =-=[1]-=- as well as the LS rank lower bound for the Pigeon-Hole Principle (PHP ) from [4]. No size lower bounds are known for LS, and it seems that the rank is the “right” complexity measure for LS in the sam... |

40 |
On the complexity of cutting planes proofs,
- Cook, Cullard, et al.
- 1987
(Show Context)
Citation Context ...erent methods for solving Integer Linear Programming The two most important ILP-based proof systems are Cutting Planes (introduced as a general method for solving ILP in [3], and as a proof system in =-=[2]-=-) and Lovász-Schrijver (introduced as a general method for solving ILP in [6], and first considered as a proof system in [8]). A number of mixtures of ILP-based proof systems and algebraic proof syst... |

29 | On the complexity of propositional calculus.
- Pudlak
- 1999
(Show Context)
Citation Context ...duced as a general method for solving ILP in [3], and as a proof system in [2]) and Lovász-Schrijver (introduced as a general method for solving ILP in [6], and first considered as a proof system in =-=[8]-=-). A number of mixtures of ILP-based proof systems and algebraic proof systems are introduced and studied in [4]. Another method for solving ILP was proposed by Sherali and Adams in [11] but has not b... |

27 | Complexity of semialgebraic proofs.
- Grigoriev, Hirsch, et al.
- 2002
(Show Context)
Citation Context ...d as a general method for solving ILP in [6], and first considered as a proof system in [8]). A number of mixtures of ILP-based proof systems and algebraic proof systems are introduced and studied in =-=[4]-=-. Another method for solving ILP was proposed by Sherali and Adams in [11] but has not been explored as a propositional proof system up to now. The SA relaxation is interesting in that it is static an... |

19 | A complexity gap for tree-resolution
- Riis
(Show Context)
Citation Context ...ropositional proof complexity. Thus our motivation was to obtain a result, similar in spirit, to the so-called “Complexity Gap theorem” for Treelike Resolution explicitly stated and proven by Riis in =-=[10]-=-: Theorem 1. Given a FO sentence ψ which fails in all finite structures, consider its translation into a propositional CNF contradiction Cψ,n where n is the size of the finite universe. Then either 1 ... |

1 |
lower bounds for the Sherali-Adams operator. To appear
- Rank
(Show Context)
Citation Context ...ed, i.e. can we replace polylog SA by linear SA? Our guess is “yes”, and it is supported by concrete examples, such as the PigeonHole Principle and the Least Number Principle (see the lower bounds in =-=[9]-=-). As a matter of fact, Martin [7] has already improved the poly-log to poly, i.e. to nα for some α, 0 < α ≤ 1. 2. Can a gap be proven for LS+, Lovász-Schrijver with semidefinite lifts? Note that suc... |