Despite recent successful real-world deployments of Stackelberg Security Games (SSGs), scale-up remains a fundamental challenge in this field. The latest techniques do not scale-up to domains where multiple defenders must coordinate time-dependent joint activities. To address this challenge, this paper presents two branch-and-price algorithms for solving SSGs, SMARTO and SMARTH, with three novel features: (i) a column-generation approach that uses an ordered network of nodes (determined by solving the traveling salesman problem) to generate individual defender strategies; (ii) exploitation of iterative reward shaping of multiple coordinating defender units to generate coordinated strategies; (iii) generation of tighter upper-bounds for pruning by solving security games that only abide by key scheduling constraints. We provide extensive experimental results and formal analyses.
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