Recent Advances in Graph Partitioning

We investigate the structural and algorithmic properties of 2-community structures in graphs introduced recently by Olsen (Math Soc Sci 66(3):331-336, 2013). A 2-community structure is a partition of a vertex set into two parts such that for each vertex the numbers of neighbours in/outside its own part and the sizes of the parts are correlated. We show that some well studied graph classes as graphs of maximum degree 3, minimum degree at least |V | − 3, trees and also others, have always a 2-community structure. Furthermore, a 2-community structure can be found in polynomial time in all these classes, even with additional request of connectivity in both parts. We introduce a concept of a weak 2-community and prove that in general graphs it is NP-complete to find a balanced weak 2-community structure with or without request for connectivity in both parts. On the other hand, we present a polynomial-time algorithm to solve the problem (without the condition for connectivity of parts) in graphs of degree at most 3.

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“…The partition of graphs have been intensively studied with various measures to evaluate their quality, see e.g. [2,7,14,17,19] for an overview.…”

Section: Introductionmentioning

confidence: 99%

Structural and Algorithmic Properties of 2-Community Structures

2017

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“…Rather, we shall see that it has to be adapted to resolve VM assignment. The GPLA attempts to solve the Graph Partitioning Problem (GPP) [2], [5], [8] by using the toolbox that incorporate stochastic Learning Automata (LA), which learn the optimal action offered by a random environment. Learning is achieved by interacting with the environment as it constantly changes and by processing the response of the environment to the actions taken.…”

Section: Proposed Vm Clustering Algorithmmentioning

confidence: 99%

On achieving intelligent traffic-aware consolidation of virtual machines in a data center using Learning Automata

Jobava

Yazidi

Oommen

et al. 2018

Journal of Computational Science

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Abstract-Cloud Computing (CC) is becoming increasingly pertinent and popular. A natural consequence of this is that many modern-day data centers experience very high internal traffic within the data centers themselves. The VMs with high mutual traffic often end up being far apart in the data center network, forcing them to communicate over unnecessarily long distances. The consequent traffic bottlenecks negatively affect both the performance of the application and the network in its entirety, posing nontrivial challenges for the administrators of these cloudbased data centers. The problem can, quite naturally, be compartmentalized into two phases which follow each other. First of all, the VMs are consolidated with a VM clustering algorithm, and this is achieved by utilizing the toolbox involving Learning Automata (LA). By mapping the clustering problem onto the Graph Partitioning (GP) problem, our LAbased solution successfully reduces the total communication cost by amounts that range between 34% to 85%. Thereafter, the resulting clusters are assigned to the server racks using a cluster placement algorithm that involves a completely different intelligent strategy, i.e., one that invokes Simulated Annealing (SA). This phase further reduces the total cost of communication by amounts that range between 89% to 99%. The analysis and results for different models and topologies demonstrate that the optimization is done in a fast and computationally-efficient way. Indeed, as far as we know, this paper pioneers the application of LA in the traffic-aware consolidation of virtual machines in data centers, and also pioneers a strategy which serializes the tools in LA and SA to optimize CC.

show abstract

“…Rather, we shall see that it has to be adapted to resolve VM assignment. The GPLA attempts to solve the Graph Partitioning Problem (GPP) [5], [11], [21] by using the toolbox that incorporate stochastic Learning Automata (LA), which learn the optimal action offered by a random environment. Learning is achieved by interacting with the environment as it constantly changes and by processing the response of the environment to the actions taken.…”

Section: Proposed Vm Clustering Algorithmmentioning

confidence: 99%

Achieving Intelligent Traffic-Aware Consolidation of Virtual Machines in a Data Center Using Learning Automata

Jobava

Yazidi

Oommen

et al. 2016

2016 8th IFIP International Conference on New Technologies, Mobility and Security (NTMS)

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Abstract-Cloud Computing (CC) is becoming increasingly pertinent and popular. A natural consequence of this is that many modern-day data centers experience very high internal traffic within the data centers themselves. The VMs with high mutual traffic often end up being far apart in the data center network, forcing them to communicate over unnecessarily long distances. The consequent traffic bottlenecks negatively affect both the performance of the application and the network in its entirety, posing non-trivial challenges for the administrators of these cloud-based data centers. The problem can, quite naturally, be compartmentalized into two phases which follow each other. First of all, the VMs are consolidated with a VM clustering algorithm, and this is achieved by utilizing the toolbox involving Learning Automata (LA). By mapping the clustering problem onto the Graph Partitioning (GP) problem, our LA-based solution successfully reduces the total communication cost by amounts that range between 34% to 85% when tested on real-life data center traffic traces. Thereafter, the resulting clusters are assigned to the server racks using a cluster placement algorithm that involves a completely different intelligent strategy, i.e., one that invokes Simulated Annealing (SA). This phase further reduces the total cost of communication by amounts that range between 89% to 99%. The analysis and results for different models and topologies demonstrate that the optimization is done in a fast and computationallyefficient way. Indeed, as far as we know, this paper pioneers the application of LA in the traffic-aware consolidation of virtual machines in data centers, and also pioneers a strategy which serializes the tools in LA and SA to optimize CC.

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Recent Advances in Graph Partitioning

Abstract: Abstract. We survey recent trends in practical algorithms for balanced graph partitioning, point to applications and discuss future research directions.

Cited by 401 publications

References 204 publications

Structural and Algorithmic Properties of 2-Community Structures

Structural and Algorithmic Properties of 2-Community Structures

On achieving intelligent traffic-aware consolidation of virtual machines in a data center using Learning Automata

Achieving Intelligent Traffic-Aware Consolidation of Virtual Machines in a Data Center Using Learning Automata

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