@article {866, title = {An Optimal Frontier of the Efficiency of Tissue P Systems with Cell Division}, journal = {Tenth Brainstorming Week on Membrane Computing}, volume = {II}, year = {2012}, month = {02/2012}, pages = {141-166}, publisher = {F{\'e}nix Editora}, address = {Seville, Spain}, abstract = {In the framework of tissue P systems with cell division, the length of communication rules provides a frontier for the tractability of decision problems. On the one hand, the limitation on the efficiency of tissue P systems with cell division and communication rules of length 1 has been established. On the other hand, polynomial time solutions to NP{\textendash}complete problems by using families of tissue P systems with cell division and communication rules of length at most 3 has been provided. In this paper, we improve the previous result by showing that the HAM-CYCLE problem can be solved in polynomial time by a family of tissue P systems with cell division by using communication rules with length at most 2. Hence, a new tractability boundary is given: passing from 1 to 2 amounts to passing from non{\textendash}efficiency to efficiency, assuming that P is different from NP.}, url = {http://www.gcn.us.es/10BWMC/10BWMCvolII/papers/mario-enrico-niall-revised.pdf}, author = {Antonio E. Porreca and Niall Murphy and Mario J. P{\'e}rez-Jim{\'e}nez} }