Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA

Schleich, Julien; Thi, Hoai An Le; Bouvry, Pascal

doi:10.1007/s10878-011-9396-0

Cited by 16 publications

(6 citation statements)

References 14 publications

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“…A dominating set DS of a graph G is a subset of nodes S ⊆ V such that every node not in S is joined to at least one member of S by some link. The domination number γ(G) is the number of nodes in the smallest dominating set for G ( [19]).…”

Section: Methodsmentioning

confidence: 99%

A Novel Banking Supervision Method Using the Minimum Dominating Set

Gogas

Papadimitriou

Matthaiou

2014

Network Models in Economics and Finance

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The magnitude of the recent financial crisis, which started from the U.S. and expanded in Europe, change the perspective on banking supervision. The recent consensus is that to preserve a healthy and stable banking network, the monitoring of all financial institutions should be under a single regulator, the Central Bank. In this paper we study the interrelations of banking institutions under the framework of Complex Networks. Specifically, our goal is to provide an auxiliary early warning system for the banking system's supervisor that would be used in addition to the existing schemes of control. We employ the Minimum Dominating Set (MDS) methodology to reveal the most strategically important banks of the banking network and use them as alarm triggers. By monitoring the MDS subset the regulators can have an overview of the whole network. Our dataset is formed from the 200 largest American banks and we examine their interconnection through their total deposits. The MDS concept is applied for the first time in this setting and the results show that it may be an essential supplementary tool to the arsenal of a Central Bank.

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Section: Methodsmentioning

confidence: 99%

A Novel Banking Supervision Method Using the Minimum Dominating Set

Gogas

Papadimitriou

Matthaiou

2014

Network Models in Economics and Finance

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“…The nonparallel DCABB algorithm for binary linear program is introduced in [17] by Le Thi and Pham, then the general cases with mixed-integer linear/nonlinear optimization are extensively developed by Niu and Pham (see e.g., [29,25,30]) where the integer variables are not supposed to be binary. There are various applications of this kind of approaches including scheduling [16], network optimization [38], cryptography [14] and finance [15,35] etc. This kind of algorithm is based on continuous representation techniques for integer set, exact penalty theorem, DC algorithm (DCA), and Branch-and-Bound scheme.…”

Section: Hybrid Model (Ilp-parse Tree Model)mentioning

confidence: 99%

A Difference-of-Convex Programming Approach With Parallel Branch-and-Bound For Sentence Compression Via A Hybrid Extractive Model

Niu,

You,

et al. 2020

Preprint

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Sentence compression is an important problem in natural language processing with wide applications in text summarization, search engine and human-AI interaction system etc. In this paper, we design a hybrid extractive sentence compression model combining a probability language model and a parse tree language model for compressing sentences by guaranteeing the syntax correctness of the compression results. Our compression model is formulated as an integer linear programming problem, which can be rewritten as a Difference-of-Convex (DC) programming problem based on the exact penalty technique. We use a well known efficient DC algorithm -DCA to handle the penalized problem for local optimal solutions. Then a hybrid global optimization algorithm combining DCA with a parallel branch-and-bound framework, namely PDCABB, is used for finding global optimal solutions. Numerical results demonstrate that our sentence compression model can provide excellent compression results evaluated by F-score, and indicate that PDCABB is a promising algorithm for solving our sentence compression model.

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“…Two proposals designed to create k-vertex connected m-vertex dominating set virtual backbones in an asynchronous and computer-effective way are presented in Leu and Chang [2011] and Schleich et al [2012]. For a more detailed explanation on CDSs, please refer to Schleich [2010].…”

Section: Fixed Transmission Rangementioning

confidence: 99%

Survey on Broadcast Algorithms for Mobile Ad Hoc Networks

Ruiz

Bouvry

2015

ACM Comput. Surv.

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Networking at any time and any place paves the way for a large number of possible applications in ad hoc networks, from disaster relief in remote areas to network extension. Thus, for the past decades, many works have been proposed trying to make ad hoc networks a reality. The importance of broadcasting in networking and the broadcast nature of the wireless medium have encouraged researchers to join their efforts on designing efficient dissemination algorithms for Mobile Ad Hoc Networks (MANETs). The many different challenges that MANETs face, such as limited network resources, network partitions, or energy restrictions, gave rise to many different approaches to overcome one or more of those problems. Therefore, literature reveals a huge variety of techniques that have been proposed for efficient message dissemination. In this article, we make an in-depth review of the existing state-of-the-art techniques, as well as propose a new taxonomy that provides a global overview of the most relevant existing algorithms.

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Solving the minimum M-dominating set problem by a continuous optimization approach based on DC programming and DCA

Cited by 16 publications

References 14 publications

A Novel Banking Supervision Method Using the Minimum Dominating Set

A Novel Banking Supervision Method Using the Minimum Dominating Set

A Difference-of-Convex Programming Approach With Parallel Branch-and-Bound For Sentence Compression Via A Hybrid Extractive Model

Survey on Broadcast Algorithms for Mobile Ad Hoc Networks

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