Polynomial and Extensible Solutions in Lock-Chart Solving

摘要

Lock-chart (also known as master-key system) solving is a process for designing mechanical keys and locks so that every key can open and be blocked in a user-defined set of locks. We present several algorithms as a result of our 3 years industrial collaboration project, chosen by their asymptotic time complexity and extensibility, which is the ability to add new keys and locks and satisfy the previously unforeseen blocking requirements. Our strongest result is a linear-time algorithm to find the largest diagonal lock-chart with a condition on mechanical properties of keys. Without these restrictions, but given a solution for master keys, the problem is translated into a maximum independent set problem and a greedy approximation is proposed. We evaluate the algorithms on a generated dataset using a non-backtracking procedure to simulate minimal extensions. Both approaches are suggested as heuristics or subroutines for a backtracking constraint satisfaction problem-based (CSP) solver.