TY - JOUR

T1 - Testing Equality in Communication Graphs

AU - Alon, Noga

AU - Efremenko, Klim

AU - Sudakov, Benny

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2017/11

Y1 - 2017/11

N2 - Let G = (V, E) be a connected undirected graph with k vertices. Suppose that on each vertex of the graph there is a player having an n -bit string. Each player is allowed to communicate with its neighbors according to a (static) agreed communication protocol, and the players must decide, deterministically, if their inputs are all equal. What is the minimum possible total number of bits transmitted in a protocol solving this problem ? We determine this minimum up to a lower order additive term in many cases. In particular, we show that it is kn/2+o(n) for any Hamiltonian k -vertex graph, and that for any 2-edge connected graph with m edges containing no two adjacent vertices of degree exceeding 2 it is mn/2+o(n). The proofs combine graph theoretic ideas with tools from additive number theory.

AB - Let G = (V, E) be a connected undirected graph with k vertices. Suppose that on each vertex of the graph there is a player having an n -bit string. Each player is allowed to communicate with its neighbors according to a (static) agreed communication protocol, and the players must decide, deterministically, if their inputs are all equal. What is the minimum possible total number of bits transmitted in a protocol solving this problem ? We determine this minimum up to a lower order additive term in many cases. In particular, we show that it is kn/2+o(n) for any Hamiltonian k -vertex graph, and that for any 2-edge connected graph with m edges containing no two adjacent vertices of degree exceeding 2 it is mn/2+o(n). The proofs combine graph theoretic ideas with tools from additive number theory.

KW - 2-connected graphs

KW - Communication complexity

KW - equality function

KW - static protocols

UR - http://www.scopus.com/inward/record.url?scp=85028573275&partnerID=8YFLogxK

U2 - 10.1109/TIT.2017.2744608

DO - 10.1109/TIT.2017.2744608

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AN - SCOPUS:85028573275

SN - 0018-9448

VL - 63

SP - 7569

EP - 7574

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 11

M1 - 8016410

ER -