Simulation DNA Algorithm of Set Covering Problem

Sticker model is imitated by using set, variable length vector and biochemistry operator instead of tube, memory strand and biochemistry experiment for the first time. Batch separation operator and electrophoresis operator are first put forward based on DNA algorithm of Set Covering Problem (SCP) based on sticker model. Expression way, calculation method and basic properties of variable length vector and the two biochemistry operators are analyzed in detail according to the characteristics of sticker model. Simulation DNA algorithm (SDA) of SCP, which can find out all optimization set coverings, is designed, where all feasible set coverings are extracted by using batch separation operator and all optimization set coverings are extracted by using electrophoresis operator. Minimal element and deriving element are first introduced. And minimal element contains a large amount of deriving elements, so the set of batch separation operator can be simplified. Less-than relation is established to simplify the set of electrophoresis operator. Therefore the use of ’minimal element’ and ’less-than’ makes SDA of SCP more effective and practical. Time complexity of SDA of SCP is proved, and it shows that SDA of SCP is an effective algorithm to solve SCP.