Randomized heuristics for the Max-Cut problem

Festa, Paola; Pardalos, Pãnos M.; Resende, Maurício G. C.; Ribeiro, Celso C.

doi:10.1080/1055678021000090033

Cited by 179 publications

(162 citation statements)

References 30 publications

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“…An overview of the state of the art for spin glass ground-state search is available in refs. 29 and 30, and for 24,31,and 32. We have recently introduced a efficient heuristic for groundstate search on signed graphs. This method is presented in ref.…”

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confidence: 97%

“…Computing this distance (called the "line index of balance" in refs. 20 and 21) is a nondeterministic polynomial-time hard problem, equivalent to a series of well-known problems, such as computing the ground state of a (nonplanar) Ising spin glass (22); solving a maximumcut (MAX-CUT) problem (23,24); or finding the best solution of an overconstrained linear system over a finite field (the so-called MAX-2XORSAT problem) (25). The equivalence with energy minimization of a spin glass has, for example, been highlighted recently in ref.…”

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confidence: 99%

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Computing global structural balance in large-scale signed social networks

Facchetti

Iacono

Altafini

2011

Proc. Natl. Acad. Sci. U.S.A.

350

285

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Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly "apparent disorder," rather than true "frustration."combinatorial optimization | social network theory O nline social networks are examples of large-scale communities of interacting individuals in which local ties between users (friend, fan, colleague, but also friend/foe, trust/distrust, etc.) give rise to a complex, multidimensional web of aggregated social behavior (1-4). For such complex networks, the emergence of global properties from local interactions is an intriguing subject, so far investigated mostly at structural and topological level (2,(5)(6)(7)(8). In social network theory (9-11), however, the content of the relationships is often even more important than their topology, and this calls for the development of appropriate analytical and computational tools, able to extrapolate content-related features out of the set of interactions of a social community. Obtaining efficient tools is particularly challenging when, as in social networks retrieved from online media, the size of the community is very big, of the order of 10 5 individuals or higher.A global property that has recently attracted some attention (1,(12)(13)(14) is determining the structural balance of a signed social network. Structural (or social) balance theory was first formulated by Heider (15) in order to understand the structure and origin of tensions and conflicts in a network of individuals whose mutual relationships are characterizable in terms of friendship and hostility. It was modeled in terms of signed graphs by Cartwright and Harary (16); see refs. 10 and 11 for an overview of the theory. The nodes of the graph represent users and the positive/ negative edges their friendly/hostile relationships. It has been known for some time how to interpret structural balance on such networks (16): The potential source of tensions are the cycles of the graph (i.e., the closed paths beginning and ending on the same node), notably those of negative sign (i.e., having an odd number of negative edges). It follows that the concept of balance is not related to the actual number of negative edges on the cycles but only to their parity; see Fig. 1 for an illustration on basic graphs. In particular, a signed graph is exactly balanced (i.e., tensions are completely absent) if and only if all its cycles are positive (16). As such, structural balance ...

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confidence: 97%

mentioning

confidence: 99%

Computing global structural balance in large-scale signed social networks

Facchetti

Iacono

Altafini

2011

Proc. Natl. Acad. Sci. U.S.A.

350

285

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“…This strategy strongly improves solution quality and reduces computation times with respect to memoryless implementations, see e.g. [1,2,9,15,18,19]. It is also an effective strategy for the implementation of parallel cooperative heuristics.…”

Section: Grasp With Path-relinkingmentioning

confidence: 99%

Efficient parallel cooperative implementations of GRASP heuristics

Ribeiro

Rosseti

2007

Parallel Computing

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We propose a parallel cooperative strategy for the implementation of the GRASP metaheuristic and we illustrate it with a GRASP with path-relinking heuristic for the 2-path network design problem. Numerical results illustrating the effectiveness of the approach are reported. We comment in detail the implementation strategies that take most advantage of the algorithm structure. Computational experiments show linear speedups on a Linux cluster with 32 machines.

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“…As one of Karps 21 NP-complete problems with numerous practical applications [7], a large number of metaheuristics have been proposed to tackle this problem, including tabu search [2], breakout local search [7], variable neighborhood search [9], scatter search [11], global equilibrium search [13], hybrid approaches [14], etc.…”

Section: Introductionmentioning

confidence: 99%

Hypervolume-Based Multi-level Algorithm for the Bi-criteria Max-Cut Problem

Xue

Zeng

et al. 2017

Communications in Computer and Information Science

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Abstract.The multi-level approach is known to be a highly effective metaheuristic framework for tackling several types of combinatorial optimization problems, which is one of the best performing approaches for the graph partitioning problems. In this paper, we integrate the multilevel approach into the hypervolume-based multi-objective local search algorithm, in order to solve the bi-criteria max-cut problem. The experimental results indicate that the proposed algorithm is very competitive, and the performance analysis sheds lights on the ways to further improvements.

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Randomized heuristics for the Max-Cut problem

Cited by 179 publications

References 30 publications

Computing global structural balance in large-scale signed social networks

Computing global structural balance in large-scale signed social networks

Efficient parallel cooperative implementations of GRASP heuristics

Hypervolume-Based Multi-level Algorithm for the Bi-criteria Max-Cut Problem

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