Chapter 28. Pseudo-Boolean and Cardinality Constraints

2021 ◽  
Author(s):  
Olivier Roussel ◽  
Vasco Manquinho
Keyword(s):  
Optimization Problems ◽  
Expressive Power ◽  
Natural Generalization ◽  
Satisfiability Problem ◽  
Weighted Sum ◽  
Inference Rules ◽  
Cardinality Constraint ◽  
Cardinality Constraints ◽  
Satisfiability Algorithms

Pseudo-Boolean and cardinality constraints are a natural generalization of clauses. While a clause expresses that at least one literal must be true, a cardinality constraint expresses that at least n literals must be true and a pseudo-Boolean constraint states that a weighted sum of literals must be greater than a constant. These contraints have a high expressive power, have been intensively studied in 0/1 programming and are close enough to the satisfiability problem to benefit from the recents advances in this field. Besides, optimization problems are naturally expressed in the pseudo-Boolean context. This chapter presents the inference rules on pseudo-Boolean constraints and demonstrates their increased inference power in comparison with resolution. It also shows how the modern satisfiability algorithms can be extended to deal with pseudo-Boolean constraints.

Role-Engineering Optimization with Cardinality Constraints and User-Oriented Mutually Exclusive Constraints

Information ◽  
2019 ◽  
Vol 10 (11) ◽  
pp. 342 ◽  
Author(s):  
Wei Sun ◽  
Hui Su ◽  
Hongbing Liu
Keyword(s):  
Access Control ◽  
Optimization Problems ◽  
Engineering System ◽  
Role Based Access Control ◽  
Control Mechanisms ◽  
Engineering Optimization ◽  
Cardinality Constraint ◽  
Cardinality Constraints ◽  
Role Mining ◽  
Clustering Problem

Role-based access control (RBAC) is one of the most popular access-control mechanisms because of its convenience for management and various security policies, such as cardinality constraints, mutually exclusive constraints, and user-capability constraints. Role-engineering technology is an effective method to construct RBAC systems. However, mining scales are very large, and there are redundancies in the mining results. Furthermore, conventional role-engineering methods not only do not consider more than one cardinality constraint, but also cannot ensure authorization security. To address these issues, this paper proposes a novel method called role-engineering optimization with cardinality constraints and user-oriented mutually exclusive constraints (REO_CCUMEC). First, we convert the basic role mining into a clustering problem, based on the similarities between users and use-partitioning and compression technologies, in order to eliminate redundancies, while maintaining its usability for mining roles. Second, we present three role-optimization problems and the corresponding algorithms for satisfying single or double cardinality constraints. Third, in order to evaluate the performance of authorizations in a role-engineering system, the maximal role assignments are implemented, while satisfying multiple security constraints. The theoretical analyses and experiments demonstrate the accuracy, effectiveness, and efficiency of the proposed method.

Boosting branch-and-bound MaxSAT solvers with clause learning

2021 ◽  
pp. 1-21
Author(s):  
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Branch And Bound ◽  
Real World ◽  
Optimization Problems ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Combinatorial Optimization Problems ◽  
Clause Learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

On the Implementation of a Logic Language for NP Search and Optimization Problems

2009 ◽  
pp. 798-804
Author(s):  
Sergio Greco ◽  
Cristian Molinaro ◽  
Irina Trubitsyna ◽  
Ester Zumpano
Keyword(s):  
Optimization Problems ◽  
Vertex Cover ◽  
Expressive Power ◽  
Stable Model ◽  
Restricted Version ◽  
Vertex Cover Problem ◽  
Cover Problem ◽  
Exclusive Disjunction

It is well known that NP search and optimization problems can be formulated as DATALOG¬ (datalog with unstratified negation; Abiteboul, Hull, & Vianu, 1994) queries under nondeterministic stable-model semantics so that each stable model corresponds to a possible solution (Gelfond & Lifschitz, 1988; Greco & Saccà, 1997; Kolaitis & Thakur, 1994). Although the use of (declarative) logic languages facilitates the process of writing complex applications, the use of unstratified negation allows programs to be written that in some cases are neither intuitive nor efficiently valuable. This article presents the logic language NP Datalog, a restricted version of DATALOG¬ that admits only controlled forms of negation, such as stratified negation, exclusive disjunction, and constraints. NP Datalog has the same expressive power as DATALOG¬, enables a simpler and intuitive formulation for search and optimization problems, and can be easily translated into other formalisms. The example below shows how the vertex cover problem can be expressed in NP Datalog.

Preserving Relationship Cardinality Constraints in Relational Schemata

2002 ◽  
pp. 66-112
Author(s):  
Dolores Cuadra ◽  
Carlos Nieto ◽  
Paloma Martinez ◽  
Elena Castro ◽  
Manuel Velasco
Keyword(s):  
Relational Model ◽  
Future Research ◽  
Methodological Framework ◽  
Cardinality Constraint ◽  
Cardinality Constraints ◽  
Active Rules ◽  
Model Following ◽  
Methodological Approaches ◽  
The Relationship ◽  
Practical Implications

This chapter is devoted to the study of the transformation of conceptual into logical schemata in a methodological framework focusing on a special ER construct: the relationship and its associated cardinality constraints. The section entitled “EER Model Revised: relationships and cardinality constraint” reviews the relationship and cardinality constraint constructs through different methodological approaches to establish the cardinality constraint definition that will be followed in next sections. The section “Transformation of EER Schemata into Relational Schemata” is related to the transformation of conceptual n-ary relationships (n³2) into the relational model following an active rules approach. Finally, several practical implications as well as future research paths are presented.

scholarly journals ON EXISTENTIAL DECLARATIONS OF INDEPENDENCE IN IF LOGIC

2013 ◽  
Vol 6 (2) ◽  
pp. 254-280 ◽  
Author(s):  
FAUSTO BARBERO
Keyword(s):  
Expressive Power ◽  
Inference Rules ◽  
Declaration Of Independence ◽  
Truth Values ◽  
First Order ◽  
If Logic ◽  
Knowledge Memory ◽  
Special Classes

AbstractWe analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of Independence-Friendly (IF) sentences; we give a syntactical criterion to decide whether a sentence beginning with such prefix exists, such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences.The main theorem defines a schema of sound and recursive inference rules; we show more explicitly what happens for some simple special classes of sentences.In the last section, we extend the main result beyond the scope of prenex sentences, in order to give a proof of the fact that the fragment of IF sentences with knowledge memory has only first-order expressive power.

scholarly journals The Power of the Weighted Sum Scalarization for Approximating Multiobjective Optimization Problems

2021 ◽  
Author(s):  
Cristina Bazgan ◽  
Stefan Ruzika ◽  
Clemens Thielen ◽  
Daniel Vanderpooten
Keyword(s):  
Best Approximation ◽  
Optimization Problems ◽  
Exact Algorithm ◽  
Approximate Algorithm ◽  
Weighted Sum ◽  
Approximation Quality ◽  
Minimization Problems ◽  
The Best Approximation ◽  
Trade Offs ◽  
Approximation Guarantee

AbstractWe determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of approximation that is specifically tailored to the multiobjective case and its inherent trade-offs between different objectives. For minimization problems, we provide an efficient algorithm that computes an approximation of a multiobjective problem by using an exact or approximate algorithm for its weighted sum scalarization. In case that an exact algorithm for the weighted sum scalarization is used, this algorithm comes arbitrarily close to the best approximation quality that is obtainable by supported solutions – both with respect to the common notion of approximation and with respect to the new multi-factor notion. Moreover, the algorithm yields the currently best approximation results for several well-known multiobjective minimization problems. For maximization problems, however, we show that a polynomial approximation guarantee can, in general, not be obtained in more than one of the objective functions simultaneously by supported solutions.

scholarly journals Leveraging Secondary Reflections and Mitigating Interference in Multi-IRS/RIS Aided Wireless Network

2021 ◽  
Author(s):  
Tu Nguyen ◽  
Diep Nguyen ◽  
Marco Di Renzo ◽  
Rui Zhang
Keyword(s):  
Optimization Problems ◽  
Phase Shifts ◽  
Base Station ◽  
Achievable Rate ◽  
Weighted Sum ◽  
Rate Maximization ◽  
Single User ◽  
Sum Rate Maximization ◽  
Weighted Sum Rate ◽  
Weighted Sum Rate Maximization

Reconfigurable surfaces (RS) have recently emerged as an enabler for smart radio environments where they are used to actively tailor/control the radio propagation (e.g., to support users under adverse channel conditions). If multiple RSs are deployed (e.g., coated on various buildings) to support different groups of users, it is critical to jointly optimize the phase-shifts of all RSs to mitigate their interference as well as to leverage the secondary reflections amongst them. Motivated by the above, this paper considers the uplink transmissions of multiple users that are grouped and supported by multiple RSs to communicate with a multi-antenna base station (BS). We first formulate two optimization problems: the weighted sum-rate maximization and the minimum achievable rate (from all users) maximization. Unlike existing works that considered single user or single RS or multiple RSs without inter-RS reflections, the considered problems require one to optimize the phase-shifts of all RSs' elements and all beamformers at the multi-antenna BS. The two problems turn out to be non-convex and thus are difficult to be solved in general. Moreover, the inter-RS reflections give rise to the coupling of the phase-shifts amongst RSs, making the optimization problems even more challenging to solve. To tackle them, we design alternating optimization algorithms that provably converge to locally optimal solutions. Simulation results reveal that by properly managing interference and leveraging the secondary reflections amongst RSs, there is a great benefit of deploying more RSs to support different groups of users and so as to achieve a higher rate per user. This gain is even more significant with a larger number of elements per RS. In contrast, without properly managing the secondary reflections, increasing the number of RSs can adversely impact the network throughput, especially for higher transmit power.<br>

Chapter 23. MaxSAT, Hard and Soft Constraints

2021 ◽  
Author(s):  
Chu Min Li ◽  
Felip Manyà
Keyword(s):  
Combinatorial Optimization ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Data Structures ◽  
Optimization Problems ◽  
Soft Constraints ◽  
Inference Rules ◽  
Combinatorial Optimization Problems ◽  
Definition Of ◽  
Hard And Soft Constraints

MaxSAT solving is becoming a competitive generic approach for solving combinatorial optimization problems, partly due to the development of new solving techniques that have been recently incorporated into modern MaxSAT solvers, and to the challenge problems posed at the MaxSAT Evaluations. In this chapter we present the most relevant results on both approximate and exact MaxSAT solving, and survey in more detail the techniques that have proven to be useful in branch and bound MaxSAT and Weighted MaxSAT solvers. Among such techniques, we pay special attention to the definition of good quality lower bounds, powerful inference rules, clever variable selection heuristics and suitable data structures. Moreover, we discuss the advantages of dealing with hard and soft constraints in the Partial MaxSAT formalims, and present a summary of the MaxSAT Evaluations that have been organized so far as affiliated events of the International Conference on Theory and Applications of Satisfiability Testing.

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