License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2019.23
URN: urn:nbn:de:0030-drops-115857
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11585/
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Louis, Anand ; Venkat, Rakesh

Planted Models for k-Way Edge and Vertex Expansion

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LIPIcs-FSTTCS-2019-23.pdf (0.5 MB)

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 >=slant 2. For a k-partition S_1, ..., S_k of the vertex set of a graph G = (V,E), the k-way edge expansion (resp. vertex expansion) of {S_1, ..., S_k} is defined as max_{i in [k]} Phi(S_i), and the balanced k-way edge expansion (resp. vertex expansion) of G is defined as min_{{S_1, ..., S_k} in P_k} max_{i in [k]} Phi(S_i) , where P_k is the set of all balanced k-partitions of V (i.e each part of a k-partition in P_k should have cardinality |V|/k), and Phi(S) denotes the edge expansion (resp. vertex expansion) of S subset V. We study a natural planted model for graphs where the vertex set of a graph has a k-partition S_1, ..., S_k such that the graph induced on each S_i has large expansion, but each S_i 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.

BibTeX - Entry

@InProceedings{louis_et_al:LIPIcs:2019:11585,
  author =	{Anand Louis and Rakesh Venkat},
  title =	{{Planted Models for k-Way Edge and Vertex Expansion}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11585},
  URN =		{urn:nbn:de:0030-drops-115857},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.23},
  annote =	{Keywords: Vertex Expansion, k-way partitioning, Semi-Random models, Planted Models, Approximation Algorithms, Beyond Worst Case Analysis}
}

Keywords: Vertex Expansion, k-way partitioning, Semi-Random models, Planted Models, Approximation Algorithms, Beyond Worst Case Analysis
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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