Louis, Anand ;
Venkat, Rakesh
Planted Models for kWay Edge and Vertex Expansion
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 2partition 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 kpartition S_1, ..., S_k of the vertex set of a graph G = (V,E), the kway edge expansion (resp. vertex expansion) of {S_1, ..., S_k} is defined as max_{i in [k]} Phi(S_i), and the balanced kway 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 kpartitions of V (i.e each part of a kpartition 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 kpartition 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 bicriteria approximation algorithms for computing the balanced kway 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 kWay Edge and Vertex Expansion}},
booktitle = {39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
pages = {23:123:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771313},
ISSN = {18688969},
year = {2019},
volume = {150},
editor = {Arkadev Chattopadhyay and Paul Gastin},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2019/11585},
URN = {urn:nbn:de:0030drops115857},
doi = {10.4230/LIPIcs.FSTTCS.2019.23},
annote = {Keywords: Vertex Expansion, kway partitioning, SemiRandom models, Planted Models, Approximation Algorithms, Beyond Worst Case Analysis}
}
04.12.2019
Keywords: 

Vertex Expansion, kway partitioning, SemiRandom models, Planted Models, Approximation Algorithms, Beyond Worst Case Analysis 
Seminar: 

39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Issue date: 

2019 
Date of publication: 

04.12.2019 