Sparsity of Lift-and-Project Cutting Planes

Through this study, equipment was developed which could work large size stones into linear and curve shaped cutting planes and cut polygonal shaped stones during the lapping and semi-finishing works which are pre-tasks to manufacture the large size building column or large size stone statue which is installed in the temple. The best is to read these instructions and follow the outline of this text. Safety of equipment could be secured using design program and structure interpreting program and productivity could be improved by reducing the required manpower and working time for rough grinding and semi-finishing works through positioning control module. This technology is expected to be utilized in manufacturing various stone equipments by applying the working path generation and oil pressure technologies as the type of NC work equipments as well as in future working area.

Download Full-text

Constraint-Propagation-Based Cutting Planes: An Application to the Resource-Constrained Project Scheduling Problem

INFORMS Journal on Computing ◽

10.1287/ijoc.1030.0043 ◽

2005 ◽

Vol 17 (1) ◽

pp. 52-65 ◽

Cited By ~ 37

Author(s):

Sophie Demassey ◽

Christian Artigues ◽

Philippe Michelon

Keyword(s):

Project Scheduling ◽

Cutting Planes ◽

Constraint Propagation ◽

Scheduling Problem ◽

Resource Constrained ◽

Resource Constrained Project Scheduling ◽

Project Scheduling Problem

Download Full-text

Strong lift-and-project cutting planes for the stable set problem

Mathematical Programming ◽

10.1007/s10107-012-0513-3 ◽

2012 ◽

Vol 141 (1-2) ◽

pp. 165-192 ◽

Cited By ~ 13

Author(s):

Monia Giandomenico ◽

Fabrizio Rossi ◽

Stefano Smriglio

Keyword(s):

Cutting Planes ◽

Stable Set ◽

Strong Lift ◽

Stable Set Problem

Download Full-text

Randomized feasible interpolation and monotone circuits with a local oracle

Journal of Mathematical Logic ◽

10.1142/s0219061318500125 ◽

2018 ◽

Vol 18 (02) ◽

pp. 1850012 ◽

Cited By ~ 1

Author(s):

Jan Krajíček

Keyword(s):

Lower Bounds ◽

Cutting Planes ◽

Communication Complexity ◽

Interpolation Theorem ◽

Proof System ◽

Symbolic Logic ◽

Approximate Counting ◽

Small Width ◽

Randomized Protocols ◽

Monotone Circuits

The feasible interpolation theorem for semantic derivations from [J. Krajíček, Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic, J. Symbolic Logic 62(2) (1997) 457–486] allows to derive from some short semantic derivations (e.g. in resolution) of the disjointness of two [Formula: see text] sets [Formula: see text] and [Formula: see text] a small communication protocol (a general dag-like protocol in the sense of Krajíček (1997) computing the Karchmer–Wigderson multi-function [Formula: see text] associated with the sets, and such a protocol further yields a small circuit separating [Formula: see text] from [Formula: see text]. When [Formula: see text] is closed upwards, the protocol computes the monotone Karchmer–Wigderson multi-function [Formula: see text] and the resulting circuit is monotone. Krajíček [Interpolation by a game, Math. Logic Quart. 44(4) (1998) 450–458] extended the feasible interpolation theorem to a larger class of semantic derivations using the notion of a real communication complexity (e.g. to the cutting planes proof system CP). In this paper, we generalize the method to a still larger class of semantic derivations by allowing randomized protocols. We also introduce an extension of the monotone circuit model, monotone circuits with a local oracle (CLOs), that does correspond to communication protocols for [Formula: see text] making errors. The new randomized feasible interpolation thus shows that a short semantic derivation (from a certain class of derivations larger than in the original method) of the disjointness of [Formula: see text], [Formula: see text] closed upwards, yields a small randomized protocol for [Formula: see text] and hence a small monotone CLO separating the two sets. This research is motivated by the open problem to establish a lower bound for proof system [Formula: see text] operating with clauses formed by linear Boolean functions over [Formula: see text]. The new randomized feasible interpolation applies to this proof system and also to (the semantic versions of) cutting planes CP, to small width resolution over CP of Krajíček [Discretely ordered modules as a first-order extension of the cutting planes proof system, J. Symbolic Logic 63(4) (1998) 1582–1596] (system R(CP)) and to random resolution RR of Buss, Kolodziejczyk and Thapen [Fragments of approximate counting, J. Symbolic Logic 79(2) (2014) 496–525]. The method does not yield yet lengths-of-proofs lower bounds; for this it is necessary to establish lower bounds for randomized protocols or for monotone CLOs.

Download Full-text

Homicide and corpse dismemberment: A study of one case

Indian Journal of Forensic and Community Medicine ◽

10.18231/j.ijfcm.2021.050 ◽

2021 ◽

Vol 8 (4) ◽

pp. 251-254

Author(s):

C BIGOT ◽

F O NGONGANG ◽

E NSEME ◽

M SOUMAH ◽

Z SANDO

Keyword(s):

Cutting Planes ◽

West African ◽

The Body ◽

Public Place ◽

Criminal Offence ◽

The West ◽

Development Context ◽

Plastic Bag ◽

African Context ◽

Mechanical Asphyxia

Homicide may be an isolated impulsive act arising from a situation or based on a previous conception, which is premeditation. Despite its nature or motivations, homicide remains a wrongful criminal act at all times and in all places. Several studies conducted in Western countries on this topic have highlighted the overriding concern of the criminal, which includes concealing the criminal offence in most cases.In Africa, apart from cases of infanticide, the discovery of the body of a homicide victim in a public place is a relatively common phenomenon, particularly if it involves mutilation.The body was examined; it was a young adult African female whose corpse was wrapped in a plastic bag. The autopsy established that the section or cutting planes were preferably lodged in the large joints.Death was caused by mechanical asphyxia. The focus of this case lies in the atypical nature of this type of postmortem manipulation in the West African context.The unusual nature of this type of homicide illustrates and underscores some reality in our development context.

Download Full-text

On Division Versus Saturation in Pseudo-Boolean Solving

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/237 ◽

2019 ◽

Author(s):

Stephan Gocht ◽

Jakob Nordström ◽

Amir Yehudayoff

Keyword(s):

Linear Programming ◽

Cutting Planes ◽

The Other ◽

Sat Solving ◽

Linear Combinations ◽

Division Rule ◽

Clause Learning

The conflict-driven clause learning (CDCL) paradigm has revolutionized SAT solving over the last two decades. Extending this approach to pseudo-Boolean (PB) solvers doing 0-1 linear programming holds the promise of further exponential improvements in theory, but intriguingly such gains have not materialized in practice. Also intriguingly, most PB extensions of CDCL use not the division rule in cutting planes as defined in [Cook et al., '87] but instead the so-called saturation rule. To the best of our knowledge, there has been no study comparing the strengths of division and saturation in the context of conflict-driven PB learning, when all linear combinations of inequalities are required to cancel variables. We show that PB solvers with division instead of saturation can be exponentially stronger. In the other direction, we prove that simulating a single saturation step can require an exponential number of divisions. We also perform some experiments to see whether these phenomena can be observed in actual solvers. Our conclusion is that a careful combination of division and saturation seems to be crucial to harness more of the power of cutting planes.

Download Full-text