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Sequential testing problem: A follow-up review

Tonguç Ünlüyurt

TL;DR

This article surveys developments on the $STP$ (Sequential Testing Problem) over the past two decades, covering new theoretical results, extensions, and applications. It organizes results by function classes (e.g., series/parallel, threshold/k-out-of-$n$, read-once) and by solution methods (approximation, adaptive submodularity, MDPs), highlighting the key notion of the adaptivity gap between adaptive and nonadaptive strategies. Major contributions include NP-hardness and approximation results for diverse settings, polynomial-time algorithms for select monotone classes, and batched/test-subset formulations (batch testing). The review also discusses practical aspects such as precedence constraints, imperfect tests, and applications to networks and databases, and outlines promising directions like robust optimization and real-data validation for cost- and dependency-aware STP variants.

Abstract

This review aims to provide a comprehensive update on the progress made on the Sequential Testing problem (STP) in the last 20 years after the review, [1] was published. Many studies have provided new theoretical results, extensions of the problem, and new applications. In this review, we pinpoint the main results and discuss the relations between the problems studied. We also provide possible research directions for the problem.

Sequential testing problem: A follow-up review

TL;DR

This article surveys developments on the (Sequential Testing Problem) over the past two decades, covering new theoretical results, extensions, and applications. It organizes results by function classes (e.g., series/parallel, threshold/k-out-of-, read-once) and by solution methods (approximation, adaptive submodularity, MDPs), highlighting the key notion of the adaptivity gap between adaptive and nonadaptive strategies. Major contributions include NP-hardness and approximation results for diverse settings, polynomial-time algorithms for select monotone classes, and batched/test-subset formulations (batch testing). The review also discusses practical aspects such as precedence constraints, imperfect tests, and applications to networks and databases, and outlines promising directions like robust optimization and real-data validation for cost- and dependency-aware STP variants.

Abstract

This review aims to provide a comprehensive update on the progress made on the Sequential Testing problem (STP) in the last 20 years after the review, [1] was published. Many studies have provided new theoretical results, extensions of the problem, and new applications. In this review, we pinpoint the main results and discuss the relations between the problems studied. We also provide possible research directions for the problem.

Paper Structure

This paper contains 17 sections, 5 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Classes of Monotone Boolean Functions
  4. Simple Series and Parallel Systems
  5. Threshold and $k$-out-of-$n$ Functions
  6. Read-Once Functions
  7. Models, Applications, Solution Methods and Results
  8. Function Evaluation
  9. Batch testing
  10. Precedence Constraints
  11. Network Connectivity
  12. General Discrete Functions
  13. Imperfect tests
  14. Finding the cause of failure
  15. Efficient Querying in Databases
  16. ...and 2 more sections

Figures (3)

  • Figure 1: A strategy for the function of Example 1.
  • Figure 2: Series-Parallel Network
  • Figure 3: A network that is not a Series-Parallel Network

Theorems & Definitions (1)

  • Example 1