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Choosing an optimal strategy for hierarchical group testing is an important problem for practitioners who are interested in disease screening with limited resources. For example, when screening for infectious diseases in large populations,…
We have a large number of samples and we want to find the infected ones using as few number of tests as possible. We can use group testing which tells about a small group of people whether at least one of them is infected. Group testing is…
This paper introduces the notion of Constrained Locating Arrays (CLAs), mathematical objects which can be used for fault localization in software testing. CLAs extend ordinary locating arrays to make them applicable to testing of systems…
We study here the semi-supervised $k$-clustering problem where information is available on whether pairs of objects are in the same or in different clusters. This information is either available with certainty or with a limited level of…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…
The problem of distributed matrix-vector product is considered, where the server distributes the task of the computation among $n$ worker nodes, out of which $L$ are compromised (but non-colluding) and may return incorrect results.…
We study the inference problem in the group testing to identify defective items from the perspective of the decision theory. We introduce Bayesian inference and consider the Bayesian optimal setting in which the true generative process of…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
In this note, we present a new adaptive algorithm for generalized group testing, which is asymptotically optimal if $d=o(\log_2|E|)$, $E$ is a set of potentially contaminated sets, $d$ is a maximal size of elements of $E$. Also, we design a…
This paper proposes a novel generalization of group testing, called multi-group testing, which relaxes the notion of "testing subset" in group testing to "testing multi-set". The generalization aims to learn more information of each item to…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
We consider a version of the classical group testing problem motivated by PCR testing for COVID-19. In the so-called tropical group testing model, the outcome of a test is the lowest cycle threshold (Ct) level of the individuals pooled…
In this paper, an exact bitwise MAP (Maximum A Posteriori) estimation algorithm for group testing problems is presented. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-disjunctive…
In this work we prove non-trivial impossibility results for perhaps the simplest non-linear estimation problem, that of {\it Group Testing} (GT), via the recently developed Madiman-Tetali inequalities. Group Testing concerns itself with…
A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…
The main goal of group testing with inhibitors (GTI) is to efficiently identify a small number of defective items and inhibitor items in a large set of items. A test on a subset of items is positive if the subset satisfies some specific…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
A classical problem in combinatorics seeks colorings of low discrepancy. More concretely, the goal is to color the elements of a set system so that the number of appearances of any color among the elements in each set is as balanced as…
The group testing problem is concerned with identifying a small set of infected individuals in a large population. At our disposal is a testing procedure that allows us to test several individuals together. In an idealized setting, a test…