Vertex Selection Heuristics in Branch-and-Bound Algorithms for the Maximum k-Plex Problem

2019 ◽  
Vol 28 (05) ◽  
pp. 1950015
Author(s):  
Kuixian Wu ◽  
Jian Gao ◽  
Rong Chen ◽  
Xianji Cui
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
Branch And Bound ◽  
State Of The Art ◽  
The State ◽  
Branch And Bound Algorithm ◽  
Sparse Graphs ◽  
Historical Information ◽  
Branch And Bound Algorithms ◽  
Heuristic Strategies

As a relaxation of clique in graph theory, k-plex is a powerful tool for analyzing social networks and identifying cohesive structures in graphs. Recently, more and more researchers have concentrated on the algorithms for the maximum k-plex problem. Among those algorithms, a branch-and-bound algorithm proposed very recently shows a good performance on solving large sparse graphs, but does not work well on social networks. In this paper, we propose two novel vertex selection heuristic strategies for branching. The first one employs historical information of vertex reduction, and the second one is a combination of the first heuristic and the degree-based approach. Intensive experiments on Facebook benchmark show that the algorithm combining our heuristics outperforms the state-of-the-art algorithms.

scholarly journals Link prediction in social networks: the state-of-the-art

2014 ◽  
Vol 58 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Peng Wang ◽  
BaoWen Xu ◽  
YuRong Wu ◽  
XiaoYu Zhou
Keyword(s):  
Social Networks ◽  
Link Prediction ◽  
State Of The Art ◽  
The State

scholarly journals Co-authorship prediction in academic social network

2019 ◽  
Author(s):  
William Takahiro Maruyama ◽  
Luciano Antonio Digiampietri
Keyword(s):  
Artificial Intelligence ◽  
Social Networks ◽  
Social Network ◽  
State Of The Art ◽  
The State ◽  
Artificial Intelligence Techniques ◽  
Academic Social Network ◽  
Academic Social Networks

The prediction of relationships in a social network is a complex and extremely useful task to enhance or maximize collaborations by indicating the most promising partnerships. In academic social networks, prediction of relationships is typically used to try to identify potential partners in the development of a project and/or co-authors for publishing papers. This paper presents an approach to predict coauthorships combining artificial intelligence techniques with the state-of-the-art metrics for link predicting in social networks.

GLOBAL OPTIMIZATION USING THE BRANCH‐AND‐BOUND ALGORITHM WITH A COMBINATION OF LIPSCHITZ BOUNDS OVER SIMPLICES

2009 ◽  
Vol 15 (2) ◽  
pp. 310-325 ◽  
Author(s):  
Remigijus Paulavičius ◽  
Julius Žilinskas
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
The Other ◽  
Branch And Bound Algorithm ◽  
Global Optimization Algorithm ◽  
Lipschitz Optimization ◽  
Branch And Bound Algorithms ◽  
Simple Bounds ◽  
Branch And Bound Techniques

Many problems in economy may be formulated as global optimization problems. Most numerically promising methods for solution of multivariate unconstrained Lipschitz optimization problems of dimension greater than 2 use rectangular or simplicial branch‐and‐bound techniques with computationally cheap, but rather crude lower bounds. The proposed branch‐and‐bound algorithm with simplicial partitions for global optimization uses a combination of 2 types of Lipschitz bounds. One is an improved Lipschitz bound with the first norm. The other is a combination of simple bounds with different norms. The efficiency of the proposed global optimization algorithm is evaluated experimentally and compared with the results of other well‐known algorithms. The proposed algorithm often outperforms the comparable branch‐and‐bound algorithms. Santrauka Daug įvairių ekonomikos uždavinių yra formuluojami kaip globaliojo optimizavimo uždaviniai. Didžioji dalis Lipšico globaliojo optimizavimo metodų, tinkamų spręsti didesnės dimensijos, t. y. n > 2, uždavinius, naudoja stačiakampį arba simpleksinį šakų ir rėžių metodus bei paprastesnius rėžius. Šiame darbe pasiūlytas simpleksinis šakų ir rėžių algoritmas, naudojantis dviejų tipų viršutinių rėžių junginį. Pirmasis yra pagerintas rėžis su pirmąja norma, kitas – trijų paprastesnių rėžių su skirtingomis normomis junginys. Gautieji eksperimentiniai pasiūlyto algoritmo rezultatai yra palyginti su kitų gerai žinomų Lipšico optimizavimo algoritmų rezultatais.

scholarly journals Speeding Up Incomplete GDL-based Algorithms for Multi-agent Optimization with Dense Local Utilities

2020 ◽  
Author(s):  
Yanchen Deng ◽  
Bo An
Keyword(s):  
Utility Function ◽  
Branch And Bound ◽  
State Of The Art ◽  
Search Space ◽  
Computational Effort ◽  
The State ◽  
Computational Overhead ◽  
Multi Agent

Incomplete GDL-based algorithms including Max-sum and its variants are important methods for multi-agent optimization. However, they face a significant scalability challenge as the computational overhead grows exponentially with respect to the arity of each utility function. Generic Domain Pruning (GDP) technique reduces the computational effort by performing a one-shot pruning to filter out suboptimal entries. Unfortunately, GDP could perform poorly when dealing with dense local utilities and ties which widely exist in many domains. In this paper, we present several novel sorting-based acceleration algorithms by alleviating the effect of densely distributed local utilities. Specifically, instead of one-shot pruning in GDP, we propose to integrate both search and pruning to iteratively reduce the search space. Besides, we cope with the utility ties by organizing the search space of tied utilities into AND/OR trees to enable branch-and-bound. Finally, we propose a discretization mechanism to offer a tradeoff between the reconstruction overhead and the pruning efficiency. We demonstrate the superiorities of our algorithms over the state-of-the-art from both theoretical and experimental perspectives.

Mixed-integer nonlinear optimization

Acta Numerica ◽  
2013 ◽  
Vol 22 ◽  
pp. 1-131 ◽  
Author(s):  
Pietro Belotti ◽  
Christian Kirches ◽  
Sven Leyffer ◽  
Jeff Linderoth ◽  
James Luedtke ◽  
...  
Keyword(s):  
Branch And Bound ◽  
Convex Functions ◽  
State Of The Art ◽  
Small Sample ◽  
The State ◽  
Decision Problems ◽  
Mixed Integer ◽  
Feasible Region ◽  
Convex Relaxations ◽  
Single Tree

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling nonlinear functions. We review models and applications of MINLP, and survey the state of the art in methods for solving this challenging class of problems.Most solution methods for MINLP apply some form of tree search. We distinguish two broad classes of methods: single-tree and multitree methods. We discuss these two classes of methods first in the case where the underlying problem functions are convex. Classical single-tree methods include nonlinear branch-and-bound and branch-and-cut methods, while classical multitree methods include outer approximation and Benders decomposition. The most efficient class of methods for convex MINLP are hybrid methods that combine the strengths of both classes of classical techniques.Non-convex MINLPs pose additional challenges, because they contain non-convex functions in the objective function or the constraints; hence even when the integer variables are relaxed to be continuous, the feasible region is generally non-convex, resulting in many local minima. We discuss a range of approaches for tackling this challenging class of problems, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non-convex structures to obtain improved convex relaxations.We finish our survey with a brief discussion of three important aspects of MINLP. First, we review heuristic techniques that can obtain good feasible solution in situations where the search-tree has grown too large or we require real-time solutions. Second, we describe an emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP. Third, we survey the state of the art in software for MINLP.

scholarly journals A Branch and Bound Approach to Solve the Preemptive Resource Leveling Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Behrouz Afshar-Nadjafi ◽  
Zeinab Khalaj ◽  
Esmaeil Mehdizadeh
Keyword(s):  
Objective Function ◽  
Branch And Bound ◽  
Project Scheduling ◽  
Branch And Bound Algorithm ◽  
Scheduling Problem ◽  
Resource Constrained ◽  
Additional Time ◽  
Resource Leveling ◽  
Branch And Bound Algorithms ◽  
Project Scheduling Problem

We study resource constrained project scheduling problem with respect to resource leveling as objective function and allowance of preemption in activities. The branch and bound algorithms proposed in previous researches on resource leveling problem do not consider preemption. So, representing a model for the problem, a branch and bound algorithm is proposed. This algorithm can handle preemption in resource leveling problem. Comparing the resource leveling problem and the preemptive resource leveling problem, it is observed that considering preemption in the problem leads to better results in the objective function. This improvement imposes additional time to solve the problem. Coding the algorithm in MATLAB and checking it on the projects with 8 and 10 activities, results show that the proposed algorithm is efficient.

A RELAX-AND-CUT ALGORITHM FOR THE KNAPSACK NODE WEIGHTED STEINER TREE PROBLEM

2008 ◽  
Vol 25 (03) ◽  
pp. 373-391 ◽  
Author(s):  
ROBERTO CORDONE ◽  
MARCO TRUBIAN
Keyword(s):  
Network Design ◽  
Cost Function ◽  
Branch And Bound ◽  
Steiner Tree ◽  
Exponential Family ◽  
Branch And Bound Algorithm ◽  
Steiner Tree Problem ◽  
Benchmark Problems ◽  
Sparse Graphs ◽  
Subtour Elimination

The Knapsack Node Weighted Steiner Tree Problem (KNWSTP) is a generalization of the Steiner Tree Problem on graphs, which takes into account the classical cost function defined on the edges, as well as a prize function defined on the vertices and a limit on the size of the solution. It has several applications to network design. We propose an exact branch-and-bound algorithm for this problem, based on a relax-and-cut approach: the algorithm relaxes an exponential family of generalized subtour elimination constraints and takes into account only the violated ones as the computation proceeds. The performance of the algorithm has been tested on a wide set of benchmark problems, up to three hundred vertices, whose structure reflects the features of the most likely applications (sparse graphs with Euclidean costs) and covers different cases with respect to the prize function (only positive, or both positive and negative prizes) and the weight threshold.

scholarly journals A partition-based branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

OR Spectrum ◽  
2021 ◽  
Author(s):  
Kai Watermeyer ◽  
Jürgen Zimmermann
Keyword(s):  
Exact Solution ◽  
Branch And Bound ◽  
Renewable Resources ◽  
State Of The Art ◽  
Branch And Bound Algorithm ◽  
Time Lags ◽  
Temporal Constraints ◽  
New Approach ◽  
Project Duration ◽  
Partially Renewable Resources

AbstractThe concept of partially renewable resources provides a general modeling framework that can be used for a wide range of different real-life applications. In this paper, we consider a resource-constrained project duration problem with partially renewable resources, where the temporal constraints between the activities are given by minimum and maximum time lags. We present a new branch-and-bound algorithm for this problem, which is based on a stepwise decomposition of the possible resource consumptions by the activities of the project. It is shown that the new approach results in a polynomially bounded depth of the enumeration tree, which is obtained by kind of a binary search. In a comprehensive experimental performance analysis, we compare our exact solution procedure with all branch-and-bound algorithms and state-of-the-art heuristics from the literature on different benchmark sets. The results of the performance study reveal that our branch-and-bound algorithm clearly outperforms all exact solution procedures. Furthermore, it is shown that our new approach dominates the state-of-the-art heuristics on well known benchmark instances.

scholarly journals Difusión de productos a través de redes sociales: una revisión bibliográfica utilizando la teoría de grafos

Respuestas ◽  
2013 ◽  
Vol 18 (2) ◽  
pp. 28-42 ◽  
Author(s):  
Sebastián Robledo-Giraldo ◽  
Néstor Darío Duque-Méndez ◽  
Jorge Iván Zuluaga-Giraldo
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
Social Networking ◽  
Small Groups ◽  
State Of The Art ◽  
Marketing Strategies ◽  
External Factors ◽  
Future Research ◽  
Redes Sociales ◽  
Internal And External Factors

 La difusión de productos a través de redes sociales es un campo de aplicación del mercadeo, donde la decisión de compra de un consumidor es influenciada por factores internos y externos como su red de conocidos y familiares. El propósito de esta investigación es identificar las principales perspectivas y plantear futuras investigaciones, apoyados en la revisión selectiva del estado del arte. Para la orientación de la búsqueda y la selección de artículos se utilizó la teoría de grafos, aprovechando las posibilidades de reconocer las conexiones entre los diferentes trabajos, arrojando para su análisis 18 artículos clásicos y 23 artículos actuales. A partir de esto se obtuvo, como resultado de la investigación, cuatro (4) estrategias de mercadeo diferentes: enfocadas a los influenciadores, a los no influenciadores, grupos pequeños y estrategias tradicionales de mercadeo.Palabras clave: difusión de productos, redes sociales, teoría de grafos. ABSTRACT  The diffusion of products through social networking is an application field of marketing, where the buying decision of a consumer is influenced by internal and external factors as their network of friends and relatives. The purpose of this research is to identify the main perspectives and propose future research, supported in state of the art selective review. As input for the orientation of search and articles selection, graph theory was used, leveraging the odds of recognizing the links among different works, providing for analysis 18 classic articles and 23 current articles. The result of the investigation showed four different marketing strategies: focused on influencers, non-influencers, small groups and traditional marketing strategies.Keywords: diffusion of products, social networks, graph theory.

scholarly journals Rumour prevention in social networks with layer 2 blockchains

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Subhasis Thakur ◽  
John G. Breslin
Keyword(s):  
Social Networks ◽  
Social Media ◽  
Social Network ◽  
State Of The Art ◽  
Privacy Preserving ◽  
The State ◽  
Media Content ◽  
The Social ◽  
Layer 2 ◽  
Art Methods

AbstractSocial bots can cause social, political, and economical disruptions by spreading rumours. The state-of-the-art methods to prevent social bots from spreading rumours are centralised and such solutions may not be accepted by users who may not trust a centralised solution being biased. In this paper, we developed a decentralised method to prevent social bots. In this solution, the users of a social network create a secure and privacy-preserving decentralised social network and may accept social media content if it is sent by its neighbour in the decentralised social network. As users only choose their trustworthy neighbours from the social network to be part of its neighbourhood in the decentralised social network, it prevents the social bots to influence a user to accept and share a rumour. We prove that the proposed solution can significantly reduce the number of users who are share rumour.

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