A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Trawling the Web for emerging cyber-communities
WWW '99 Proceedings of the eighth international conference on World Wide Web
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Greedily finding a dense subgraph
Journal of Algorithms
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
A Polylogarithmic Approximation of the Minimum Bisection
SIAM Journal on Computing
On cutting a few vertices from a graph
Discrete Applied Mathematics
On the densest k-subgraph problems
On the densest k-subgraph problems
Structural and algorithmic aspects of massive social networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithm Design
ACM Transactions on Algorithms (TALG)
A unified platform for data driven web applications with automatic client-server partitioning
Proceedings of the 16th international conference on World Wide Web
Pricing of partially compatible products
Proceedings of the 8th ACM conference on Electronic commerce
Approximation Algorithms for the Firefighter Problem: Cuts over Time and Submodularity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Better vaccination strategies for better people
Proceedings of the 11th ACM conference on Electronic commerce
Approximating minimum cut with bounded size
INOC'11 Proceedings of the 5th international conference on Network optimization
Approximation algorithms and hardness of the k-route cut problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximating maximum cut with limited unbalance
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Approximation algorithms for fragmenting a graph against a stochastically-located threat
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
SIAM Journal on Computing
On the inapproximability of minimizing cascading failures under the deterministic threshold model
Information Processing Letters
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We introduce the Minimum-size bounded-capacity cut (MinSBCC) problem, in which we are given a graph with an identified source and seek to find a cut minimizing the number of nodes on the source side, subject to the constraint that its capacity not exceed a prescribed bound B. Besides being of interest in the study of graph cuts, this problem arises in many practical settings, such as in epidemiology, disaster control, military containment, as well as finding dense subgraphs and communities in graphs. In general, the MinSBCC problem is NP-complete. We present an efficient $(\frac{1}{{\rm \lambda}},\frac{1}{1-{\rm \lambda}})$-bicriteria approximation algorithm for any 0 λ B. In fact, the algorithm’s solution either violates the budget constraint, or exceeds the optimal number of source-side nodes, but not both. For graphs of bounded treewidth, we show that the problem with unit weight nodes can be solved optimally in polynomial time, and when the nodes have weights, approximated arbitrarily well by a PTAS.