The constraint satisfaction problem (CSP) is among the most studied computational
problems. While NP-hard, many tractable subproblems have been identified (Bulatov 2017,
Zuk 2017). Backdoors, introduced by Williams, Gomes, and Selman (2003), gradually
extend such a tractable class to all CSP instances of bounded distance to the class.
Backdoor size provides a natural but rather crude distance measure between a CSP
instance and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and …

The constraint satisfaction problem (CSP) is among the most studied computational
problems. While NP-hard, many tractable subproblems have been identified (Bulatov, Zhuk)
Backdoors, introduced by Williams, Gomes, and Selman, gradually extend such a tractable
class to all CSP instances of bounded distance to the class. Backdoor size provides a
natural but rather crude distance measure between a CSP instance and a tractable class.
Backdoor depth, introduced by Mählmann, Siebertz, and Vigny for SAT, is a more refined …