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Planted Models for k-Way Edge and Vertex Expansion Louis, Anand Venkat, Rakesh Vertex Expansion k-way partitioning Semi-Random models Planted Models Approximation Algorithms Beyond Worst Case Analysis 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anand Louis and Rakesh Venkat 2019 Is Part Of LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2019.23 urn:nbn:de:0030-drops-115857 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.23 eng https://creativecommons.org/licenses/by/3.0/legalcode