Improved approximations of crossings in graph drawings
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
The directed circular arrangement problem
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
l22 spreading metrics for vertex ordering problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Inoculation strategies for victims of viruses and the sum-of-squares partition problem
Journal of Computer and System Sciences
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A linear-time algorithm to find a separator in a graph excluding a minor
ACM Transactions on Algorithms (TALG)
Pairwise data clustering and applications
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Hierarchical density-based clustering of categorical data and a simplification
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
The directed circular arrangement problem
ACM Transactions on Algorithms (TALG)
Fast approximate correlation for massive time-series data
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Better vaccination strategies for better people
Proceedings of the 11th ACM conference on Electronic commerce
On approximation of new optimization methods for assessing network vulnerability
INFOCOM'10 Proceedings of the 29th conference on Information communications
On the minimum load coloring problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Advantage of overlapping clusters for minimizing conductance
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Streaming graph partitioning for large distributed graphs
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast balanced partitioning is hard even on grids and trees
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Design principles for packet parsers
ANCS '13 Proceedings of the ninth ACM/IEEE symposium on Architectures for networking and communications systems
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We study graph partitioning problems on graphs with edge capacities and vertex weights. The problems of b-balanced cuts and k-balanced partitions are unified into a new problem called minimum capacity $\rho$-separators. A $\rho$-separator is a subset of edges whose removal partitions the vertex set into connected components such that the sum of the vertex weights in each component is at most $\rho$ times the weight of the graph. We present a new and simple O(log n)-approximation algorithm for minimum capacity $\rho$-separators which is based on spreading metrics yielding an O(log n)-approximation algorithm both for b-balanced cuts and k-balanced partitions. In particular, this result improves the previous best known approximation factor for k-balanced partitions in undirected graphs by a factor of O(log k). We enhance these results by presenting a version of the algorithm that obtains an O(log OPT)-approximation factor. The algorithm is based on a technique called spreading metrics that enables us to formulate directly the minimum capacity $\rho$-separator problem as an integer program. We also introduce a generalization called the simultaneous separator problem, where the goal is to find a minimum capacity subset of edges that separates a given collection of subsets simultaneously. We extend our results to directed graphs for values of $\rho \geq 1/2$. We conclude with an efficient algorithm for computing an optimal spreading metric for $\rho$-separators. This yields more efficient algorithms for computing b-balanced cuts than were previously known.