Combinatorial Group Testing and Sparse Recovery Schemes with Near-Optimal Decoding Time

06/15/2020
by   Mahdi Cheraghchi, et al.
0

In the long-studied problem of combinatorial group testing, one is asked to detect a set of k defective items out of a population of size n, using m ≪ n disjunctive measurements. In the non-adaptive setting, the most widely used combinatorial objects are disjunct and list-disjunct matrices, which define incidence matrices of test schemes. Disjunct matrices allow the identification of the exact set of defectives, whereas list disjunct matrices identify a small superset of the defectives. Apart from the combinatorial guarantees, it is often of key interest to equip measurement designs with efficient decoding algorithms. The most efficient decoders should run in sublinear time in n, and ideally near-linear in the number of measurements m. In this work, we give several constructions with an optimal number of measurements and near-optimal decoding time for the most fundamental group testing tasks, as well as for central tasks in the compressed sensing and heavy hitters literature. For many of those tasks, the previous measurement-optimal constructions needed time either quadratic in the number of measurements or linear in the universe size. Most of our results are obtained via a clean and novel approach which avoids list-recoverable codes or related complex techniques which were present in almost every state-of-the-art work on efficiently decodable constructions of such objects.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/09/2021

Near optimal efficient decoding from pooled data

The objective of the pooled data problem is to design a measurement matr...
research
01/29/2021

Combinatorial Quantitative Group Testing with Adversarially Perturbed Measurements

In this paper, combinatorial quantitative group testing (QGT) with noisy...
research
05/29/2018

Sublinear decoding schemes for non-adaptive group testing with inhibitors

Identification of up to d defective items and up to h inhibitors in a se...
research
12/05/2017

Deterministic Heavy Hitters with Sublinear Query Time

This paper studies the classic problem of finding heavy hitters in the t...
research
12/20/2022

Efficient Algorithms for the Bee-Identification Problem

The bee-identification problem, formally defined by Tandon, Tan and Vars...
research
02/09/2022

Group testing via residuation and partial geometries

The motivation for this paper comes from the ongoing SARS-CoV-2 Pandemic...
research
01/29/2023

Combinatorial Pen Testing (or Consumer Surplus of Deferred-Acceptance Auctions)

Pen testing is the problem of selecting high capacity resources when the...

Please sign up or login with your details

Forgot password? Click here to reset