Optimal speedup of Las Vegas algorithms
Information Processing Letters
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
What is answer set programming?
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
DNA origami as self-assembling circuit boards
UC'10 Proceedings of the 9th international conference on Unconventional computation
Synthesizing minimal tile sets for patterned DNA self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Synthesis of Tile Sets for DNA Self-Assembly
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Theory of algorithmic self-assembly
Communications of the ACM
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Synthesizing minimal tile sets for complex patterns in the framework of patterned DNA self-assembly
Theoretical Computer Science
Search methods for tile sets in patterned DNA self-assembly
Journal of Computer and System Sciences
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We consider the problem of finding, for a given 2D pattern of colored tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of Winfree (1998). This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös and Orponen (2011), who presented an exhaustive partition-search branch-and-bound algorithm (briefly PS-BB) for it. However, finding the true minimal tile sets is very time consuming, and PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partition-search framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel instances of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. We also introduce a method for computing the reliability of a tile set, i.e. the probability of its error-free self-assembly to the target tiling, based on Winfree's analysis of the kinetic Tile Assembly Model (1998). We present data on the reliability of tile sets found by the algorithms and find that also here PS-H constitutes a significant improvement over PS-BB.