TY - JOUR
T1 - Number on the Forehead Protocols yielding dense Ruzsa–Szemerédi graphs and hypergraphs
AU - Alon, N.
AU - Shraibman, A.
N1 - Publisher Copyright:
© 2020, Akadémiai Kiadó, Budapest, Hungary.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - We describe algorithmic Number On the Forehead protocols thatprovide dense Ruzsa–Szemerédi graphs. One protocol leads to a simple and natural extension of the original construction of Ruzsa and Szemerédi.The graphs induced by this protocol have n vertices, Ω (n2/ log n) edges, and are decomposable into n1+O(1/loglogn) induced matchings.Another protocol is a somewhat simpler version of theconstruction of [1], producing graphs with similar properties.We also generalize the above protocols to morethan three players, in orderto construct dense uniformhypergraphs in which every edge lies in a positivesmall number of simplices, extending a result of Fox and Loh.
AB - We describe algorithmic Number On the Forehead protocols thatprovide dense Ruzsa–Szemerédi graphs. One protocol leads to a simple and natural extension of the original construction of Ruzsa and Szemerédi.The graphs induced by this protocol have n vertices, Ω (n2/ log n) edges, and are decomposable into n1+O(1/loglogn) induced matchings.Another protocol is a somewhat simpler version of theconstruction of [1], producing graphs with similar properties.We also generalize the above protocols to morethan three players, in orderto construct dense uniformhypergraphs in which every edge lies in a positivesmall number of simplices, extending a result of Fox and Loh.
KW - NOF protocol
KW - Ruzsa–Szemerédi graph
KW - communication complexity
KW - induced matching
UR - http://www.scopus.com/inward/record.url?scp=85088482355&partnerID=8YFLogxK
U2 - 10.1007/s10474-020-01069-8
DO - 10.1007/s10474-020-01069-8
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AN - SCOPUS:85088482355
SN - 0236-5294
VL - 161
SP - 488
EP - 506
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
IS - 2
ER -