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Short Survey on Graph Correlation Clustering with Minimization Criteria

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Discrete Optimization and Operations Research (DOOR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

In clustering problems one has to partition a given set of objects into some subsets (called clusters) taking into consideration only similarity of the objects. One of the most visual formalizations of clustering is the graph clustering, that is, grouping the vertices of a graph into clusters taking into consideration the edge structure of the graph whose vertices are objects and edges represent similarities between the objects.

In this short survey, we consider the graph correlation clustering problems where the goal is to minimize the number of edges between clusters and the number of missing edges inside clusters. We present a number of results on graph correlation clustering including results on computational complexity and approximability of different variants of the problems, and performance guarantees of approximation algorithms for graph correlation clustering. Some results on approximability of weighted versions of graph correlation clustering are also presented.

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Acknowledgements

The research of the first and the third authors (Sects. 1–4, 6, 7) was supported by the RSF grant 15-11-10009.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090, Novosibirsk, Russia

    Victor Il’ev & Alexander Kononov

  2. Omsk State University, 55a Mira Avenue, 644077, Omsk, Russia

    Victor Il’ev & Svetlana Il’eva

Authors
  1. Victor Il’ev
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  2. Svetlana Il’eva
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  3. Alexander Kononov
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Correspondence to Victor Il’ev .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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Il’ev, V., Il’eva, S., Kononov, A. (2016). Short Survey on Graph Correlation Clustering with Minimization Criteria. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_3

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