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
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This content will become publicly available on October 15, 2026
Verifying a Sparse Matrix Algorithm Using Symbolic Execution
Scientific software is, by its very nature, complex. It is mathematical and highly optimized which makes it prone to subtle bugs not as easily detected by traditional testing. We outline how symbolic execution can be used to write tests similar to traditional unit tests while providing stronger verification guarantees and apply this methodology to a sparse matrix algorithm.
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- Award ID(s):
- 1955852
- PAR ID:
- 10650050
- Editor(s):
- Siegel, Stephen F; Gopalakrishnan, Ganesh
- Publisher / Repository:
- EPTCS
- Date Published:
- Journal Name:
- Electronic Proceedings in Theoretical Computer Science
- Volume:
- 432
- ISSN:
- 2075-2180
- Page Range / eLocation ID:
- 27 to 36
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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