Group testing is a technique that can reduce the number of tests needed to identify infected members in a population, by pooling together multiple diagnostic samples. Despite the variety and importance of prior results, traditional work on group testing has typically assumed independent infections. However, contagious diseases among humans, like SARS-CoV-2, have an important characteristic: infections are governed by community spread, and are therefore correlated. In this paper, we explore this observation and we argue that taking into account the community structure when testing can lead to significant savings in terms of the number of tests required to guarantee a given identification accuracy. To show that, we start with a simplistic (yet practical) infection model, where the entire population is organized in (possibly overlapping) communities and the infection probability of an individual depends on the communities (s)he participates in. Given this model, we compute new lower bounds on the number of tests for zero-error identification and design community-aware group testing algorithms that can be optimal under assumptions. Finally, we demonstrate significant benefits over traditional, community-agnostic group testing via simulations using both noiseless and noisy tests. Shorter versions of this article, which contained a subset of the material, were presented in the work by Nikolopoulos et al. (2021, 2021).

We study the problem of group testing with non-identical, independent priors. So far, the pooling strategies that have been proposed in the literature take the following approach: a hand-crafted test design along with a decoding strategy is proposed, and guarantees are provided on how many tests are sufficient in order to identify all infections in a population. In this paper, we take a different, yet perhaps more practical, approach: we fix the decoder and the number of tests, and we ask, given these, what is the best test design one could use? We explore this question for the Definite Non-Defectives (DND) decoder. We formulate a (non-convex) optimization problem, where the objective function is the expected number of errors for a particular design. We find approximate solutions via gradient descent, which we further optimize with informed initialization. We illustrate through simulations that our method can achieve significant performance improvement over traditional approaches.

In this paper, we introduce a "discrete-time SIR stochastic block model" that also allows for group testing and interventions on a daily basis. Our model can be regarded as a discrete version of the well-known continuous-time SIR stochastic network model [1] and relies on a specific type of weighted graph to capture the underlying community spread. Given that infection model, we then formulate a dynamic group-testing problem by asking: (a) what is the minimum number of tests needed everyday to identify all infections? and (b) are there nonadaptive group testing strategies that achieve this with vanishing error probability? Our results show that one can leverage the knowledge of the community infection model to compute a lower bound on the number of tests and also inform nonadaptive group testing algorithms, so that they can achieve (almost) the same performance as complete individual testing with a much smaller number of tests. Moreover, these algorithms are order-optimal, under specific conditions.

In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection probability depends on the community (s)he participates in. Use cases include families, students who participate in several classes, and workers who share common spaces. Group testing reduces the number of tests needed to identify the infected individuals by pooling diagnostic samples and testing them together. We show that if we design the testing strategy taking into account the community structure, we can significantly reduce the number of tests needed for adaptive and non-adaptive group testing, and can improve the reliability in cases where tests are noisy.

In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and the infection probability of each individual depends on the communities (s)he participates in. Use cases include students who participate in several classes, and workers who share common spaces. Group testing reduces the number of tests needed to identify the infected individuals by pooling diagnostic samples and testing them together. We show that making testing algorithms aware of the community structure, can significantly reduce the number of tests needed both for adaptive and non-adaptive group testing.

SIR (Susceptible, Infected or Recovered) stochastic network models are commonly used to describe the progression of epidemics inside a network. A task of interest in epidemiology is to use these models to estimate the state evolution, both at an individual as well as a population level. In this paper, we propose using continual testing to improve the state estimation at the individual level. Our testing is inspired from entropy reduction principles and requires only a small number of tests.

Sequencing a DNA strand, as part of the read process in DNA storage, produces multiple noisy copies which can be combined to produce better estimates of the original strand; this is called trace reconstruction. One can reduce the error rate further by introducing redundancy in write sequence and this is called coded trace reconstruction. In this paper, we model the DNA storage channel as an insertion-deletion-substitution (IDS) channel and design both encoding schemes and low-complexity decoding algorithms for coded trace reconstruction. We introduce Trellis BMA, a new reconstruction algorithm whose complexity is linear in the number of traces, and compare its performance to previous algorithms. Our results show that it reduces the error rate on both simulated and experimental data. The performance comparisons in this paper are based on the Clustered Nanopore Reads Dataset publicly released with this paper. Our hope is that this dataset will enable research progress by allowing objective comparisons between candidate algorithms.

Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion channels, a notoriously difficult problem due to its highly combinatorial nature. Although works in theoretical computer science have provided algorithms which guarantee perfect reconstruction with multiple independent observations from the deletion channel, they are only applicable in the large blocklength regime and more restrictively, when the number of observations is also large. Indeed, with only a few observations, perfect reconstruction of the input sequence may not even be possible in most cases. In such situations, maximum likelihood (ML) and maximum aposteriori (MAP) estimates for the deletion channels are natural questions that arise and these have remained open to the best of our knowledge. In this work, we take steps to answer the two aforementioned questions. Specifically: 1. We show that solving for the ML estimate over the single deletion channel (which can be cast as a discrete optimization problem) is equivalent to solving its relaxation, a continuous optimization problem; 2. We exactly compute the symbolwise posterior distributions (under some assumptions on the priors) for both the single as well as multiple deletion channels. As part of our contributions, we also introduce tools to visualize and analyze error events, which we believe could be useful in other related problems concerning deletion channels.

Maximum likelihood (ML) and symbolwise maximum aposteriori (MAP) estimation for discrete input sequences play a central role in a number of applications that arise in communications, information and coding theory. Many instances of these problems are proven to be intractable, for example through reduction to NP-complete integer optimization problems. In this work, we prove that the ML estimation of a discrete input sequence (with no assumptions on the encoder/channel used) is equivalent to the solution of a continuous non-convex optimization problem, and that this formulation is closely related to the computation of symbolwise MAP estimates. This equivalence is particularly useful in situations where a function we term the expected likelihood is efficiently computable. In such situations, we give a ML heuristic and show numerics for sequence estimation over the deletion channel.

We consider the problem of reconstructing a sequence from fixed number of deleted versions of itself (also called traces). The problem is motivated from recent developments in de novo DNA sequencing technologies. The main contribution of this work is to provide a polynomial time algorithm for symbolwise MAP decoding with multiple traces. The algorithm leverages a dynamic program on the edit graph. We also develop a heuristic with reduced time complexity using similar ideas and provide preliminary numerical evaluations.

The problem of reconstructing a sequence when observed through multiple looks over deletion channels occurs in “de novo” DNA sequencing. The DNA could be sequenced multiple times, yielding several “looks” of it, but each time the sequencer could be noisy with (independent) deletion impairments. The main goal of this paper is to develop reconstruction algorithms for a sequence observed through the lens of a fixed number of deletion channels. We use the probabilistic model of the deletion channels to develop both symbol-wise and sequence maximum likelihood decoding criteria, and algorithms motivated by them. Numerical evaluations demonstrate improvement in terms of edit distance error, over earlier algorithms.

Trade-offs between distributed computation and communication are recently attracting significant interest; however, these works assume that all nodes that share the distributed computation task are within the same broadcast domain, and each can losslessly broadcast to every other node that takes part in the computation task. In this work, we dispose of this assumption, and consider the case where each node can broadcast to a subset of the nodes that take part in the computation task. We model the network via an Erdos-Renyi random graph model where a pair of nodes can communicate with each other with a probability p. We propose both uncoded and coded transmission schemes and give an achievable communication-computation tradeoff for large computational loads.

In wireless distributed computing, networked nodes perform intermediate computations over data placed in their memory and exchange these intermediate values to calculate function values. In this paper we consider an asymmetric setting where each node has access to a random subset of the data, i.e., we cannot control the data placement. The paper makes a simple point: we can realize significant benefits if we are allowed to be “flexible”, and decide which node computes which function, in our system. We make this argument in the case where each function depends on only two of the data messages, as is the case in similarity searches. We establish a percolation in the behaviour of the system, where, depending on the amount of observed data, by being flexible, we may need no communication at all.