Improved approximations of packing and covering problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
On the bias of traceroute sampling: or, power-law degree distributions in regular graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
DIMES: let the internet measure itself
ACM SIGCOMM Computer Communication Review
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Three Approximation Algorithms for Energy-Efficient Query Dissemination in Sensor Database System
DEXA '09 Proceedings of the 20th International Conference on Database and Expert Systems Applications
Primitives for active internet topology mapping: toward high-frequency characterization
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
Toward fast and efficient IP-level network topology capture
Proceedings of the 2012 ACM conference on CoNEXT student workshop
Efficient IP-Level network topology capture
PAM'13 Proceedings of the 14th international conference on Passive and Active Measurement
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In highly distributed Internet measurement systems distributed agents periodically measure the Internet using a tool called traceroute, which discovers a path in the network graph. Each agent performs many traceroute measurements to a set of destinations in the network, and thus reveals a portion of the Internet graph as it is seen from the agent locations. In every period we need to check whether previously discovered edges still exist in this period, a process termed validation. To this end we maintain a database of all the different measurements performed by each agent. Our aim is to be able to validate the existence of all previously discovered edges in the minimum possible time. In this work we formulate the validation problem as a generalization of the well know set cover problem. We reduce the set cover problem to the validation problem, thus proving that the validation problem is NP-hard. We present a O(logn)-approximation algorithm to the validation problem, where n in the number of edges that need to be validated. We also show that unless P=NP the approximation ratio of the validation problem is @W(logn).