Adjacency Sketches in Adversarial Environments
Moni Naor, Eugene Pekel

TL;DR
This paper studies the resilience of probabilistic adjacency sketches in graphs against adaptive adversaries, establishing tight bounds on label sizes related to the maximum degree of the graph.
Contribution
It introduces a new analysis of adjacency sketches under adaptive adversarial queries, showing a tight relationship between label size and maximum degree.
Findings
Constructed sketches that fail with probability ε using 2d log(1/ε) bits for graphs with max degree d.
Proved this bound is nearly optimal for specific graphs like d-ary trees.
Established a stronger characterization of adjacency sketches in adversarial settings.
Abstract
An adjacency sketching or implicit labeling scheme for a family of graphs is a method that defines for any vertex an assignment of labels to each vertex in , so that the labels of two vertices tell you whether or not they are adjacent. The goal is to come up with labeling schemes that use as few bits as possible to represent the labels. By using randomness when assigning labels, it is sometimes possible to produce adjacency sketches with much smaller label sizes, but this comes at the cost of introducing some probability of error. Both deterministic and randomized labeling schemes have been extensively studied, as they have applications for distributed data structures and deeper connections to universal graphs and communication complexity. The main question of interest is which graph families have schemes using short labels, usually in the…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Cryptography and Data Security · Privacy-Preserving Technologies in Data
