TY - GEN
T1 - Approximation algorithms for semi-random partitioning problems
AU - Makarychev, Konstantin
AU - Makarychev, Yury
AU - Vijayaraghavan, Aravindan
PY - 2012
Y1 - 2012
N2 - In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real-world instances. The model is more flexible than the semi-random model of Feige and Kilian and planted random model of Bui, Chaudhuri, Leighton and Sipser. We develop a general framework for solving semi-random instances and apply it to several problems of interest. We present constant factor bi-criteria approximation algorithms for semi-random instances of the Balanced Cut, Multicut, Min Uncut, Sparsest Cut and Small Set Expansion problems. We also show how to almost recover the optimal solution if the instance satisfies an additional expanding condition. Our algorithms work in a wider range of parameters than most algorithms for previously studied random and semi-random models. Additionally, we study a new planted algebraic expander model and develop constant factor bi-criteria approximation algorithms for graph partitioning problems in this model.
AB - In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real-world instances. The model is more flexible than the semi-random model of Feige and Kilian and planted random model of Bui, Chaudhuri, Leighton and Sipser. We develop a general framework for solving semi-random instances and apply it to several problems of interest. We present constant factor bi-criteria approximation algorithms for semi-random instances of the Balanced Cut, Multicut, Min Uncut, Sparsest Cut and Small Set Expansion problems. We also show how to almost recover the optimal solution if the instance satisfies an additional expanding condition. Our algorithms work in a wider range of parameters than most algorithms for previously studied random and semi-random models. Additionally, we study a new planted algebraic expander model and develop constant factor bi-criteria approximation algorithms for graph partitioning problems in this model.
KW - approximation algorithm
KW - average-case analysis
KW - graph partitioning
KW - random planted model
KW - semi-random model
UR - http://www.scopus.com/inward/record.url?scp=84862617734&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84862617734&partnerID=8YFLogxK
U2 - 10.1145/2213977.2214013
DO - 10.1145/2213977.2214013
M3 - Conference contribution
AN - SCOPUS:84862617734
SN - 9781450312455
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 367
EP - 384
BT - STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing
T2 - 44th Annual ACM Symposium on Theory of Computing, STOC '12
Y2 - 19 May 2012 through 22 May 2012
ER -