TY - GEN
T1 - The communication complexity of approximate set packing and covering
AU - Nisan, Noam
PY - 2002
Y1 - 2002
N2 - We consider a setting where k players are each holdingsome collection of subsets of {1..n}. We consider the communication complexity of approximately solvingt wo problems: The cover number: the minimal number of sets (in the union of their collections) whose union is {1...n} and the packing number: the maximum number of sets (in the union of their collections) that are pair-wise disjoint. We prove that while computinga (ln n)-approximation for the cover number and an min(κ,O( √ n))-approximation for the packingn umber can be done with polynomial (in n) amount of communication, getting a (1/2 - ε) log n approximation for the cover number or a better than min(κ, n1/2-ε)-approximation for the packingn umber requires exponential communication complexity.
AB - We consider a setting where k players are each holdingsome collection of subsets of {1..n}. We consider the communication complexity of approximately solvingt wo problems: The cover number: the minimal number of sets (in the union of their collections) whose union is {1...n} and the packing number: the maximum number of sets (in the union of their collections) that are pair-wise disjoint. We prove that while computinga (ln n)-approximation for the cover number and an min(κ,O( √ n))-approximation for the packingn umber can be done with polynomial (in n) amount of communication, getting a (1/2 - ε) log n approximation for the cover number or a better than min(κ, n1/2-ε)-approximation for the packingn umber requires exponential communication complexity.
UR - http://www.scopus.com/inward/record.url?scp=84869159580&partnerID=8YFLogxK
U2 - 10.1007/3-540-45465-9_74
DO - 10.1007/3-540-45465-9_74
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AN - SCOPUS:84869159580
SN - 3540438645
SN - 9783540438649
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 868
EP - 875
BT - Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
A2 - Widmayer, Peter
A2 - Eidenbenz, Stephan
A2 - Triguero, Francisco
A2 - Morales, Rafael
A2 - Conejo, Ricardo
A2 - Hennessy, Matthew
PB - Springer Verlag
T2 - 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002
Y2 - 8 July 2002 through 13 July 2002
ER -