Semi-random graphs with planted sparse vertex cuts: Algorithms for exact and approximate recovery

Louis, A and Venkat, R (2018) Semi-random graphs with planted sparse vertex cuts: Algorithms for exact and approximate recovery. In: 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, 9 - 13 July 2018, Prague.

PDF ICALP_2018.pdf - Published Version Restricted to Registered users only Download (571kB) | Request a copy

Abstract

The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a O log n-approximation algorithm due to Feige et al. 16, and O OPT log d bound in graphs having vertex degrees at most d due to Louis et al. 29. We study a natural semi-random model of graphs with sparse vertex cuts. For certain ranges of parameters, we give an algorithm to recover the planted sparse vertex cut exactly. For a larger range of parameters, we give a constant factor bi-criteria approximation algorithm to compute the graph's balanced vertex expansion. Our algorithms are based on studying a semidefinite programming relaxation for the balanced vertex expansion of the graph. In addition to being a family of instances that will help us to better understand the complexity of the computation of vertex expansion, our model can also be used in the study of community detection where only a few nodes from each community interact with nodes from other communities. There has been a lot of work on studying random and semi-random graphs with planted sparse edge cuts. To the best of our knowledge, our model of semi-random graphs with planted sparse vertex cuts has not been studied before.

Item Type:	Conference Paper
Publication:	Leibniz International Proceedings in Informatics, LIPIcs
Publisher:	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information:	The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Keywords:	Approximation algorithms; Automata theory; Computational complexity; Expansion; Graphic methods; Parameter estimation, Bi-criteria; Community detection; Constant factors; Semi-definite programming relaxations; Semi-random models; Vertex degree; Vertex expansions; Worst-case analysis, Graph theory
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	08 Aug 2022 10:39
Last Modified:	08 Aug 2022 10:39
URI:	https://eprints.iisc.ac.in/id/eprint/75492

Actions (login required)

View Item