TY - JOUR

T1 - A Θ (log n)-approximation for the set cover problem with set ownership

AU - Gonen, Mira

AU - Shavitt, Yuval

N1 - Funding Information:
This research was supported in part under ISF grant number 8008, and by the Yeshaya Horowitz Association through the Center for Complexity Science.

PY - 2009/1/16

Y1 - 2009/1/16

N2 - 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 (log n)-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 Ω (log n).

AB - 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 (log n)-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 Ω (log n).

KW - Approximation algorithms

KW - Internet

KW - Measurement systems

KW - Traceroute

UR - http://www.scopus.com/inward/record.url?scp=57349124917&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2008.09.023

DO - 10.1016/j.ipl.2008.09.023

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AN - SCOPUS:57349124917

SN - 0020-0190

VL - 109

SP - 183

EP - 186

JO - Information Processing Letters

JF - Information Processing Letters

IS - 3

ER -