Group Testing with Two and Three Defectives

  title={Group Testing with Two and Three Defectives},
  author={X. M. Chang and F. Hwang and J. Weng},
  journal={Annals of the New York Academy of Sciences},
Consider a population of n items consisting of d defectives and n d good ones. The problem is to find the d defectives by means of a sequence of group tests. We will call a set of items contaminated if it contains a t least one defective, pure if it contains no defective, and free if there is no information on it. Then a group test is a test on a given set with two possible outcomes: the set is identified either as a contaminated set or as a pure set. Let M,(d, n ) be the maximum number of… Expand
Quaternary splitting algorithm in group testing
  • Jinn Lu, H. Fu
  • Computer Science, Mathematics
  • J. Comb. Optim.
  • 2021
This paper focuses on estimating M ( d,  n ) and obtaining a better result than known ones in various cases of d and n and denotes the minimum number of tests in the worst case situation. Expand
An Efficient Algorithm for Combinatorial Group Testing
  • Andreas Allemann
  • Mathematics, Computer Science
  • Information Theory, Combinatorics, and Search Theory
  • 2013
A new algorithm which in the worst case needs less than $0.255d+\frac{1}{2}\log d+5.5$ tests more than the information lower bound for n/d≥2 and the behaviour for large n and d of the difference is optimal for $\frac{n}{d}\leq4$. Expand
Competitive Group Testing
  • D. Du, F. Hwang
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 1993
This paper presents some competitive group testing algorithms and defines M(n,d) = minA MA(n), the maximum number of group tests for a group testing algorithm A to identify d defectives from a set of n items when d is known. Expand
Group testing problem with two defectives
A new adaptive algorithm is proposed such that for N = 2 + 1 - t - t 2 - t 4, the problem of finding two defectives among N elements can be solved in t tests. Expand
Updating a Tale of Two Coins
The criterion used to evaluate a procedure A for a model M is the worst case number of tests required to detect the two irregulars among n items, denoted by T,(n). Expand
An NP-Completeness Result of Edge Search in Graphs
  • T. Gerzen
  • Mathematics, Computer Science
  • Graphs Comb.
  • 2014
The present paper shows that the computation of cp(G), which contains n vertices two of which are defective and adjacent, is an NP-complete problem, and establishes some results on it for random graphs. Expand
A group testing problem for graphs with several defective edges
  • Petra Johann
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 2002
This paper proves the conjecture that finding all defective edges by testing whether an induced subgraph contains a defective edge or not can be done by using at most d log 2 m d +c tests for some constant c. Expand
Improved upper bounds for several variants of group testing
Sequential Algorithms for Special Cases


An optimal search procedure
Abstract Consider the following problem. There are exactly two defective (unknown) elements in the set X ={ x 1 , x 2 ,…, x n }, all possibilities occuring with equal probabilities. We want toExpand
A Group Testing Problem on Two Disjoint Sets
Recently the following group testing problem has been studied. We have two disjoint sets of items with cardinalities m and n respectively, where each set is known to contain exactly one defectiveExpand
Group testing with two defectives
This paper gives a partial solution to the problem of determining the minimax number of group tests for finding two defectives separately contained in two disjoint sets. Expand
Binomial and Hypergeometric Group-Testing