8 research outputs found
A Breezing Proof of the KMW Bound
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW)
proved a hardness result for several fundamental graph problems in the LOCAL
model: For any (randomized) algorithm, there are input graphs with nodes
and maximum degree on which (expected) communication rounds are
required to obtain polylogarithmic approximations to a minimum vertex cover,
minimum dominating set, or maximum matching. Via reduction, this hardness
extends to symmetry breaking tasks like finding maximal independent sets or
maximal matchings. Today, more than years later, there is still no proof
of this result that is easy on the reader. Setting out to change this, in this
work, we provide a fully self-contained and proof of the KMW
lower bound. The key argument is algorithmic, and it relies on an invariant
that can be readily verified from the generation rules of the lower bound
graphs.Comment: 21 pages, 6 figure
Purple Patcher 1969
This is a digitized version of the 1969 Purple Patcher. Physical copies of the Purple Patcher are held by the College of the Holy Cross Archives.https://crossworks.holycross.edu/purple_patcher/1029/thumbnail.jp
Winona Daily News
https://openriver.winona.edu/winonadailynews/1941/thumbnail.jp
Winona Daily News
https://openriver.winona.edu/winonadailynews/1880/thumbnail.jp
A Breezing Proof of the {KMW} Bound
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with nodes and maximum degree on which (expected) communication rounds are required to obtain polylogarithmic approximations to a minimum vertex cover, minimum dominating set, or maximum matching. Via reduction, this hardness extends to symmetry breaking tasks like finding maximal independent sets or maximal matchings. Today, more than years later, there is still no proof of this result that is easy on the reader. Setting out to change this, in this work, we provide a fully self-contained and proof of the KMW lower bound. The key argument is algorithmic, and it relies on an invariant that can be readily verified from the generation rules of the lower bound graphs
University of San Diego News Print Media Coverage 1987.03
Printed clippings housed in folders with a table of contents arranged by topic.https://digital.sandiego.edu/print-media/1216/thumbnail.jp