CHEN HO-LINDoty, D.D.DotySeki, S.S.Seki2018-09-102018-09-10201103029743http://www.scopus.com/inward/record.url?eid=2-s2.0-84055191080&partnerID=MN8TOARShttp://scholars.lib.ntu.edu.tw/handle/123456789/362545https://www.scopus.com/inward/record.uri?eid=2-s2.0-84055191080&doi=10.1007%2f978-3-642-25591-5_46&partnerID=40&md5=d0b6eb1530c15072a0033ee774ec25beWinfree's abstract Tile Assembly Model (aTAM) is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing "seed" assembly based on specific binding sites on their four sides. We show that there is a polynomial-time algorithm that, given an n ×n square, finds the minimal tile system (i.e., the system with the smallest number of distinct tile types) that uniquely self-assembles the square, answering an open question of Adleman, Cheng, Goel, Huang, Kempe, Moisset de Espanés, and Rothemund (Combinatorial Optimization Problems in Self-Assembly, STOC 2002). Our investigation leading to this algorithm reveals other positive and negative results about the relationship between the size of a tile system and its "temperature" (the binding strength threshold required for a tile to attach) © 2011 Springer-Verlag.Assembly model; Binding strength; Combinatorial optimization problems; DNA complex; Molecular self assembly; Polynomial-time algorithms; Program size; Specific binding; Binding sites; Combinatorial optimization; Self assembly; Algorithmsconference paper10.1007/978-3-642-25591-5_462-s2.0-84055191080