The Communication Complexity of Approximate Set Packing and Covering

  • Noam Nisan
Conference paper

DOI: 10.1007/3-540-45465-9_74

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)
Cite this paper as:
Nisan N. (2002) The Communication Complexity of Approximate Set Packing and Covering. In: Widmayer P., Eidenbenz S., Triguero F., Morales R., Conejo R., Hennessy M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg

Abstract

We consider a setting where k players are each holding some collection of subsets of 1..n. We consider the communication complexity of approximately solving two 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 computing a (ln n)-approximation for the cover number and an min(k, O(√n))-approximation for the packing number can be done with polynomial (in n) amount of communication, getting a (1/2 − ε) logn approximation for the cover number or a better than min(k, n1/2 − ε)-approximation for the packing number requires exponential communication complexity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Noam Nisan
    • 1
  1. 1.Institute of Computer ScienceThe Hebrew University of JerusalemIsrael

Personalised recommendations