The most basic lower-bound question in randomized communication complexity is: Does a
given problem have constant cost, or non-constant cost? We observe that this question has …

We study the two-player communication problem of determining whether two vertices $ x, y $
are nearby in a graph $ G $, with the goal of determining the graph structures that allow the …

How to efficiently represent a graph in computer memory is a fundamental data structuring
question. In the present paper, we address this question from a combinatorial point of view …

A class of graphs admits an adjacency labeling scheme of size $ f (n) $, if the vertices of any
$ n $-vertex graph $ G $ in the class can be assigned binary strings (aka labels) of length $ f …

A labeling scheme is a space-efficient data structure for encoding graphs from a particular
graph class. The idea is to assign each vertex of a graph a short label st adjacency of two …

In this work, we provide an upper bound for global certification of graph homomorphism, a
generalization of graph coloring. In certification, the nodes of a network should decide if the …

We prove that the class of communication problems with public-coin randomized constant-
cost protocols, called BPP 0, does not contain a complete problem. In other words, there is …

Local certification is the area of distributed network computing asking the following question:
How to certify to the nodes of a network that a global property holds, if they are limited to a …

Every known communication problem whose randomized communication cost is constant
(independent of the input size) can be reduced to $ k $-Hamming Distance, that is, solved …

In this work, we provide an upper bound for global certification of graph homomorphism, a
generalization of graph coloring. In certification, the nodes of a network should decide if the …