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In this paper, we investigate the problem of assigning scan cells to multiple scan chains based on physical placement. We formulate a new multichain assignment (MA) problem and discuss its complexity and relationship to partitioning and traveling salesman problems. We show that MA is not adequately solved by approaches based on the traveling salesman methods alone and present two new algorithms for MA based on partitioning and stable marriage (SM) problems. We demonstrate that even though partitioning-based methods offer significant improvements compared to previous methods, the SM-based algorithm offers the best results. We compare our algorithms with previous work based on preplacement and greedy assignments in terms of total scan net lengths and maximum load capacitance of scan cells. Experiments with ISCAS89 benchmarks indicate that our algorithms improve the chain lengths 50%-90%, while reducing the maximum load capacitance by 30%-50%.