Improving heuristics for network modularity maximization using an exact algorithm

Cafieri, Sonia; Hansen, Pierre; Liberti, Leo

doi:10.1016/j.dam.2012.03.030

Cited by 27 publications

(25 citation statements)

References 48 publications

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“…Results are shown in Table 2. Results for the Zachary and Dolphins benchmarks match the highly refined values reported in [30] which, to our knowledge are the "best" in the literature ever obtained. The quantum annealer performs slightly better for the Dolphins network, when compared with non-refined results in the literature [41].…”

Section: Resultssupporting

confidence: 81%

Detecting multiple communities using quantum annealing on the D-Wave system

2020

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A very important problem in combinatorial optimization is partitioning a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences. The problem of community detection is a twofold problem that consists of determining the number of communities and, at the same time, finding those communities. This drastically increases the solution space for heuristics to work on, compared to traditional graph partitioning problems. In many of the scientific domains in which graphs are used, there is the need to have the ability to partition a graph into communities with the "highest quality" possible since the presence of even small isolated communities can become crucial to explain a particular phenomenon. We have explored community detection using the power of quantum annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out that the problem of detecting at most two communities naturally fits into the architecture of a quantum annealer with almost no need of reformulation. This paper addresses a systematic study of detecting two or more communities in a network us-ing a quantum annealer.

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Section: Resultssupporting

confidence: 81%

Detecting multiple communities using quantum annealing on the D-Wave system

2020

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“…Therefore, the SFC placement problem is also NP-Hard. The method to solve this problem can be divided into two categories: an exact algorithm and a heuristic algorithm [20]. The exact algorithm has limited applicability due to its computational complexity.…”

Section: Integer Linear Programming (Ilp) Formulationmentioning

confidence: 99%

A Dynamic Placement Mechanism of Service Function Chaining Based on Software-defined Networking

2018

KSII TIIS

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To cope with the explosive growth of Internet services, Service Function Chaining (SFC) based on Software-defined Networking (SDN) is an emerging and promising technology that has been suggested to meet this challenge. Determining the placement of Virtual Network Functions (VNFs) and routing paths that optimize the network utilization and resource consumption is a challenging problem, particularly without violating service level agreements (SLAs). This problem is called the optimal SFC placement problem and an Integer Linear Programming (ILP) formulation is provided. A greedy heuristic solution is also provided based on an improved two-step mapping algorithm. The obtained experimental results show that the proposed algorithm can automatically place VNFs at the optimal locations and find the optimal routing paths for each online request. This algorithm can increase the average request acceptance rate by about 17.6% and provide more than 20-fold reduction of the computational complexity compared to the Greedy algorithm. The feasibility of this approach is demonstrated via NetFPGA-10G prototype implementation.

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“…Based on the concept of modularity, the problem of community detection becomes equivalent to modularity optimization. Therefore, several methods have been proposed to find the optimal solution with the lowest computational cost [3,6,10,15,17,33,32,40]. Fortunato and Barthélemy [12] found that such modularity contains an intrinsic scale that depends on the total size of links in a network.…”

Section: Introductionmentioning

confidence: 99%

Density-based modularity for evaluating community structure in bipartite networks

Chen

et al. 2015

Information Sciences

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Improving heuristics for network modularity maximization using an exact algorithm

Cited by 27 publications

References 48 publications

Detecting multiple communities using quantum annealing on the D-Wave system

Detecting multiple communities using quantum annealing on the D-Wave system

A Dynamic Placement Mechanism of Service Function Chaining Based on Software-defined Networking

Density-based modularity for evaluating community structure in bipartite networks

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