Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Approximating the minimum degree spanning tree to within one from the optimal degree
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Almost tight bounds for &egr;-nets
Discrete & Computational Geometry
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
A Polylogarithmic Approximation of the Minimum Bisection
SIAM Journal on Computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On the complexity of finding balanced oneway cuts
Information Processing Letters
Network failure detection and graph connectivity
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
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The Valve Location Problem in Simple Network Topologies
Graph-Theoretic Concepts in Computer Science
A linear-time algorithm to find a separator in a graph excluding a minor
ACM Transactions on Algorithms (TALG)
The valve location problem: Minimizing environmental damage of a spill in long oil pipelines
Computers and Industrial Engineering
Discrete Applied Mathematics
Algorithms for multiterminal cuts
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
The Valve Location Problem in Simple Network Topologies
INFORMS Journal on Computing
How to cut a graph into many pieces
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
FPTASs for trimming weighted trees
Theoretical Computer Science
On the parameterized complexity of finding separators with non-hereditary properties
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
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Let G be an n-vertex graph that has a vertex separator of size k that partitions the graph into connected components of size smaller than α n, for some fixed 2/3 ≤ α unless the graph contains an (α+ε)-separator of size strictly less than k, in which case our algorithm finds one such separator. For fixed ε, the running time of our algorithm is nO(1)2O(k), which is polynomial for k = O(log n). For bounded degree graphs (as well as for the case of finding balanced edge separators), we present a deterministic algorithm with similar running time.Our algorithm involves (among other things) a new concept that we call (ε,k)-samples. This is related to the notion of detection sets for network failures, introduced by Kleinberg [FOCS 2000]. Our proofs adapt and simplify techniques that were introduced by Kleinberg. As a by-product, our proof improves the known bounds on the size of detection sets. We also show applications of (ε,k)-samples to problems in approximation algorithms and rigorous analysis of heuristics.