On the Erdős covering problem: the density of the uncovered set

2021 ◽  
Author(s):  
Paul Balister ◽  
Béla Bollobás ◽  
Robert Morris ◽  
Julian Sahasrabudhe ◽  
Marius Tiba
Keyword(s):  
Covering Problem ◽  
Uncovered Set

Uncovered set choice rules

2007 ◽  
Vol 31 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Michele Lombardi
Keyword(s):  
Uncovered Set

scholarly journals Prosociality in Majority Decisions: A Laboratory Experiment on the Robustness of the Uncovered Set

2021 ◽  
pp. 1-14
Author(s):  
Jan Sauermann
Keyword(s):  
Majority Rule ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Behavioral Model ◽  
Uncovered Set ◽  
Multiple Dimensions ◽  
Self Interest ◽  
Empirical Perspective ◽  
Committee Decision Making ◽  
Policy Shifts

Abstract Social choice theory demonstrates that majority rule is generically indeterminate. However, from an empirical perspective, large and arbitrary policy shifts are rare events in politics. The uncovered set (UCS) is the dominant preference-based explanation for the apparent empirical predictability of majority rule in multiple dimensions. Its underlying logic assumes that voters act strategically, considering the ultimate consequences of their actions. I argue that all empirical applications of the UCS rest on an incomplete behavioral model assuming purely egoistically motivated individuals. Beyond material self-interest, prosocial motivations offer an additional factor to explain the outcomes of majority rule. I test my claim in a series of committee decision-making experiments in which I systematically vary the fairness properties of the policy space while keeping the location of the UCS constant. The experimental results overwhelmingly support the prosociality explanation.

scholarly journals Q-Learnheuristics: Towards Data-Driven Balanced Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1839
Author(s):  
Broderick Crawford ◽  
Ricardo Soto ◽  
José Lemus-Romani ◽  
Marcelo Becerra-Rozas ◽  
José M. Lanza-Gutiérrez ◽  
...  
Keyword(s):  
Combinatorial Problems ◽  
Set Covering ◽  
Covering Problem ◽  
Integration Framework ◽  
Q Learning ◽  
Whale Optimization ◽  
Sine Cosine Algorithm ◽  
Exploration Exploitation ◽  
Selection Of

One of the central issues that must be resolved for a metaheuristic optimization process to work well is the dilemma of the balance between exploration and exploitation. The metaheuristics (MH) that achieved this balance can be called balanced MH, where a Q-Learning (QL) integration framework was proposed for the selection of metaheuristic operators conducive to this balance, particularly the selection of binarization schemes when a continuous metaheuristic solves binary combinatorial problems. In this work the use of this framework is extended to other recent metaheuristics, demonstrating that the integration of QL in the selection of operators improves the exploration-exploitation balance. Specifically, the Whale Optimization Algorithm and the Sine-Cosine Algorithm are tested by solving the Set Covering Problem, showing statistical improvements in this balance and in the quality of the solutions.

scholarly journals An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 225
Author(s):  
José García ◽  
Gino Astorga ◽  
Víctor Yepes
Keyword(s):  
Transfer Functions ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Set Covering ◽  
Covering Problem ◽  
Perturbation Operator ◽  
K Nearest Neighbors ◽  
Combinatorial Optimization Problems ◽  
Box Plots ◽  
Metaheuristic Techniques

The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.

scholarly journals A fast $$(2 + \frac{2}{7})$$-approximation algorithm for capacitated cycle covering

2021 ◽  
Author(s):  
Vera Traub ◽  
Thorben Tröbst
Keyword(s):  
Vehicle Routing Problem ◽  
Covering Problem ◽  
Post Processing ◽  
Routing Problem ◽  
Cycle Cover ◽  
Disjoint Cycles ◽  
Processing Step ◽  
Number Of Cycles ◽  
Vertex Disjoint ◽  
Capacitated Vehicle

AbstractWe consider the capacitated cycle covering problem: given an undirected, complete graph G with metric edge lengths and demands on the vertices, we want to cover the vertices with vertex-disjoint cycles, each serving a demand of at most one. The objective is to minimize a linear combination of the total length and the number of cycles. This problem is closely related to the capacitated vehicle routing problem (CVRP) and other cycle cover problems such as min-max cycle cover and bounded cycle cover. We show that a greedy algorithm followed by a post-processing step yields a $$(2 + \frac{2}{7})$$ ( 2 + 2 7 ) -approximation for this problem by comparing the solution to a polymatroid relaxation. We also show that the analysis of our algorithm is tight and provide a $$2 + \epsilon $$ 2 + ϵ lower bound for the relaxation.

scholarly journals A Self-Adaptive Cuckoo Search Algorithm Using a Machine Learning Technique

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1840
Author(s):  
Nicolás Caselli ◽  
Ricardo Soto ◽  
Broderick Crawford ◽  
Sergio Valdivia ◽  
Rodrigo Olivares
Keyword(s):  
Machine Learning ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Cuckoo Search Algorithm ◽  
Set Covering ◽  
Covering Problem ◽  
Parameter Configuration ◽  
Self Tuning ◽  
Problem Solvers

Metaheuristics are intelligent problem-solvers that have been very efficient in solving huge optimization problems for more than two decades. However, the main drawback of these solvers is the need for problem-dependent and complex parameter setting in order to reach good results. This paper presents a new cuckoo search algorithm able to self-adapt its configuration, particularly its population and the abandon probability. The self-tuning process is governed by using machine learning, where cluster analysis is employed to autonomously and properly compute the number of agents needed at each step of the solving process. The goal is to efficiently explore the space of possible solutions while alleviating human effort in parameter configuration. We illustrate interesting experimental results on the well-known set covering problem, where the proposed approach is able to compete against various state-of-the-art algorithms, achieving better results in one single run versus 20 different configurations. In addition, the result obtained is compared with similar hybrid bio-inspired algorithms illustrating interesting results for this proposal.

scholarly journals Multi-objective database queries in combined knapsack and set covering problem domains

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Sean A. Mochocki ◽  
Gary B. Lamont ◽  
Robert C. Leishman ◽  
Kyle J. Kauffman
Keyword(s):  
Relational Database ◽  
Set Covering ◽  
Covering Problem ◽  
Set Covering Problem ◽  
Database Queries ◽  
Multi Objective ◽  
Data Representations ◽  
Np Hard Problem ◽  
Institute Of Technology ◽  
The One

AbstractDatabase queries are one of the most important functions of a relational database. Users are interested in viewing a variety of data representations, and this may vary based on database purpose and the nature of the stored data. The Air Force Institute of Technology has approximately 100 data logs which will be converted to the standardized Scorpion Data Model format. A relational database is designed to house this data and its associated sensor and non-sensor metadata. Deterministic polynomial-time queries were used to test the performance of this schema against two other schemas, with databases of 100 and 1000 logs of repeated data and randomized metadata. Of these approaches, the one that had the best performance was chosen as AFIT’s database solution, and now more complex and useful queries need to be developed to enable filter research. To this end, consider the combined Multi-Objective Knapsack/Set Covering Database Query. Algorithms which address The Set Covering Problem or Knapsack Problem could be used individually to achieve useful results, but together they could offer additional power to a potential user. This paper explores the NP-Hard problem domain of the Multi-Objective KP/SCP, proposes Genetic and Hill Climber algorithms, implements these algorithms using Java, populates their data structures using SQL queries from two test databases, and finally compares how these algorithms perform.

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