Sphere Packing and Local Majorities in Graphs.

Nathan Linial, David Peleg, Yuri Rabinovich, Michael E. Saks

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The paper concerns some extremal problems on packing spheres in graphs and covering graphs by spheres. Tight bounds are provided for these problems on general graphs. The bounds are then applied to answer the following question: Let f be a nonnegative function defined on the vertices of a graph G, and suppose one has a lower bound on the local averages of f, i.e., on f's average over every j-neighborhood in G for j=1,. . .,r. What can be concluded globally? I.e, what can be said about the average of f over all G? This question arose in connection with issues of locality in distributed network computation. The average estimation problem with unit radius balls is also studied for some special classes of graphs.
Original languageEnglish
Title of host publication2nd Israel Symposium on Theory and Computing Systems
Subtitle of host publicationISTCS 1993
PublisherIEEE Computer Society
Number of pages9
ISBN (Print)0-8186-3630-0
StatePublished - 1993
Event2nd Israel Symposium on Theory and Computing Systems, ISTCS 1993 - Natanya, Israel
Duration: 7 Jun 19939 Jun 1993
Conference number: 2


Conference2nd Israel Symposium on Theory and Computing Systems, ISTCS 1993
Abbreviated titleISTCS 1993
Internet address


  • Computational geometry
  • Graph coloring


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