Hypercubes and Multicommodity Flows
SIAM Journal on Discrete Mathematics
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Fast Approximate Graph Partitioning Algorithms
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
l22 spreading metrics for vertex ordering problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
How to Play Unique Games Using Embeddings
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Theory of Computing Systems
An improved approximation ratio for the minimum linear arrangement problem
Information Processing Letters
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
Simple cuts are fast and good: optimum right-angled cuts in solid grids
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Surviving failures in bandwidth-constrained datacenters
Proceedings of the ACM SIGCOMM 2012 conference on Applications, technologies, architectures, and protocols for computer communication
Fast balanced partitioning is hard even on grids and trees
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Surviving failures in bandwidth-constrained datacenters
ACM SIGCOMM Computer Communication Review - Special october issue SIGCOMM '12
ACM Transactions on Embedded Computing Systems (TECS)
FENNEL: streaming graph partitioning for massive scale graphs
Proceedings of the 7th ACM international conference on Web search and data mining
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We consider the k-balanced partitioning problem, where the goal is to partition the vertices of an input graph G into k equally sized components, while minimizing the total weight of the edges connecting different components. We allow k to be part of the input and denote the cardinality of the vertex set by n. This problem is a natural and important generalization of well-known graph partitioning problems, including minimum bisection and minimum balanced cut. We present a (bi-criteria) approximation algorithm achieving an approximation of O(√log n log k), which matches or improves over previous algorithms for all relevant values of k. Our algorithm uses a semidefinite relaxation which combines l22 metrics with spreading metrics. Surprisingly, we show that the integrality gap of the semidefinite relaxation is Ω(log k) even for large values of k (e.g., k = nΩ(1), implying that the dependence on k of the approximation factor is necessary. This is in contrast to previous approximation algorithms for k-balanced partitioning, which are based on linear programming relaxations and their approximation factor is independent of k.