Louis, A and Venkat, R
(2019)
*Planted models for k-way edge and vertex expansion.*
In: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2019, 11-13 December 2019, Institute of Technology BombayBombay; India.

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## Abstract

Graph partitioning problems are a central topic of study in algorithms and complexity theory. Edge expansion and vertex expansion, two popular graph partitioning objectives, seek a 2-partition of the vertex set of the graph that minimizes the considered objective. However, for many natural applications, one might require a graph to be partitioned into k parts, for some k > 2. For a k-partition S1,..., Sk of the vertex set of a graph G = (V, E), the k-way edge expansion (resp. vertex expansion) of S1,..., Sk is defined as maxiâ��k Î¦(Si), and the balanced k-way edge expansion (resp. vertex expansion) of G is defined as min {S1,...,Sk}â��Pk max iâ��k Î¦(Si) , where Pk is the set of all balanced k-partitions of V (i.e each part of a k-partition in Pk should have cardinality |V |/k), and Î¦(S) denotes the edge expansion (resp. vertex expansion) of S â�� V. We study a natural planted model for graphs where the vertex set of a graph has a k-partition S1,..., Sk such that the graph induced on each Si has large expansion, but each Si has small edge expansion (resp. vertex expansion) in the graph. We give bi-criteria approximation algorithms for computing the balanced k-way edge expansion (resp. vertex expansion) of instances in this planted model.

Item Type: | Conference Paper |
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Publication: | Leibniz International Proceedings in Informatics, LIPIcs |

Publisher: | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Additional Information: | Copyright of this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Keywords: | Approximation algorithms; Computational complexity; Expansion; Silicon; Software engineering, Algorithms and complexity; Cardinalities; Edge expansion; Graph Partitioning; Graph partitioning problems; Semi-random models; Vertex expansions; Worst-case analysis, Graph theory |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 26 Feb 2020 10:13 |

Last Modified: | 26 Feb 2020 10:13 |

URI: | http://eprints.iisc.ac.in/id/eprint/64372 |

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