Network failure detection and graph connectivity
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Semi-supervised learning using randomized mincuts
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Finding small balanced separators
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Catching elephants with mice: sparse sampling for monitoring sensor networks
Proceedings of the 5th international conference on Embedded networked sensor systems
Detecting cuts in sensor networks
ACM Transactions on Sensor Networks (TOSN)
The Cost of Learning Directed Cuts
ECML '07 Proceedings of the 18th European conference on Machine Learning
Catching elephants with mice: Sparse sampling for monitoring sensor networks
ACM Transactions on Sensor Networks (TOSN)
A discriminative model for semi-supervised learning
Journal of the ACM (JACM)
VC-dimension and shortest path algorithms
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the complexity of finding an unknown cut via vertex queries
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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Measuring the properties of a large, unstructured network can be difficult: one may not have full knowledge of the network topology, and detailed global measurements may be infeasible. A valuable approach to such problems is to take measurements from selected locations within the network and then aggregate them to infer large-scale properties. One sees this notion applied in settings that range from Internet topology discovery tools to remote software agents that estimate the download times of popular Web pages. Some of the most basic questions about this type of approach, however, are largely unresolved at an analytical level. How reliable are the results? How much does the choice of measurement locations affect the aggregate information one infers about the network? We describe algorithms that yield provable guarantees for a particular problem of this type: detecting a network failure. Suppose we want to detect events of the following form: an adversary destroys up to k nodes or edges, after which two subsets of the nodes, each at least an /spl epsi/ fraction of the network, are disconnected from one another. We call such an event an (/spl epsi/,k) partition. One method for detecting such events would be to place "agents" at a set D of nodes, and record a fault whenever two of them become separated from each other. To be a good detection set, D should become disconnected whenever there is an (/spl epsi/,k)-partition; in this way, it "witnesses" all such events. We show that every graph has a detection set of size polynomial in k and /spl epsi//sup -1/, and independent of the size of the graph itself. Moreover, random sampling provides an effective way to construct such a set. Our analysis establishes a connection between graph separators and the notion of VC-dimension, using techniques based on matchings and disjoint paths.