Sphere Packing and Local Majorities in Graphs.

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

doi:10.1109/ISTCS.1993.253475

Sphere Packing and Local Majorities in Graphs.

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

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
Title of host publication	2nd Israel Symposium on Theory and Computing Systems
Subtitle of host publication	ISTCS 1993
Publisher	IEEE Computer Society
Pages	141-149
Number of pages	9
ISBN (Print)	0-8186-3630-0
DOIs	https://doi.org/10.1109/ISTCS.1993.253475
State	Published - 1993
Event	2nd Israel Symposium on Theory and Computing Systems, ISTCS 1993 - Natanya, Israel Duration: 7 Jun 1993 → 9 Jun 1993 Conference number: 2 https://www.computer.org/csdl/proceedings/istcs/1993/12OmNyS6RMM

Conference

Conference	2nd Israel Symposium on Theory and Computing Systems, ISTCS 1993
Abbreviated title	ISTCS 1993
Country/Territory	Israel
City	Natanya
Period	7/06/93 → 9/06/93
Internet address	https://www.computer.org/csdl/proceedings/istcs/1993/12OmNyS6RMM

Keywords

Computational geometry
Graph coloring

Access to Document

10.1109/ISTCS.1993.253475

http://doi.ieeecomputersociety.org/10.1109/ISTCS.1993.253475

Cite this

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title = "Sphere Packing and Local Majorities in Graphs.",

abstract = "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.",

keywords = "Computational geometry, Graph coloring",

author = "Nathan Linial and David Peleg and Yuri Rabinovich and Saks, {Michael E.}",

year = "1993",

doi = "10.1109/ISTCS.1993.253475",

language = "אנגלית",

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pages = "141--149",

booktitle = "2nd Israel Symposium on Theory and Computing Systems",

publisher = "IEEE Computer Society",

address = "ארצות הברית",

note = "2nd Israel Symposium on Theory and Computing Systems, ISTCS 1993 ; Conference date: 07-06-1993 Through 09-06-1993",

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N2 - 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.

AB - 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.

KW - Computational geometry

KW - Graph coloring

U2 - 10.1109/ISTCS.1993.253475

DO - 10.1109/ISTCS.1993.253475

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BT - 2nd Israel Symposium on Theory and Computing Systems

PB - IEEE Computer Society

T2 - 2nd Israel Symposium on Theory and Computing Systems, ISTCS 1993

Y2 - 7 June 1993 through 9 June 1993

ER -

Sphere Packing and Local Majorities in Graphs.

Abstract

Conference

Keywords

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