Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a permutation $\pi$, the application of prefix reversal $f^{(i)}$ to $\pi$ reverses the order of the first $i$ elements of $\pi$. The problem of sorting by prefix reversals (also known as pancake flipping), made famous by Gates and Papadimitriou (Discrete Math., 27 (1979), pp. 47-57), asks for the minimum number of prefix reversals required to sort the elements of a given permutation.   study a variant of this problem where the prefix reversals act not on permutations but on strings over a fixed size alphabet.  determine the minimum number of prefix reversals required to sort binary and ternary strings, with polynomial-time algorithms for these sorting problems as a result; demonstrate that computing the minimum prefix reversal distance beten two binary strings is NP-hard; give an exact expression for the prefix reversal diameter of binary strings; and give bounds on the prefix reversal diameter of ternary strings.  also consider a aker form of sorting called grouping (of identical symbols) and give polynomial-time algorithms for optimally grouping binary and ternary strings. A number of intriguing open problems are also discussed.
['Caj Cor Hurkens', 'Leo van Iersel', 'Jcm Judith Keijsper', 'Sm Kelk', 'Leen Stougie', 'Jt Tromp']
I am writing a research paper on a idea Prefix Reversals on Binary and Ternary Strings
[{"from": "human", "value": "I am writing a research paper on a idea Prefix Reversals on Binary and Ternary Strings"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a permutation $\\pi$, the application of prefix reversal $f^{(i)}$ to $\\pi$ reverses the order of the first $i$ elements of $\\pi$. The problem of sorting by prefix reversals (also known as pancake flipping), made famous by Gates and Papadimitriou (Discrete Math., 27 (1979), pp. 47-57), asks for the minimum number of prefix reversals required to sort the elements of a given permutation.   study a variant of this problem where the prefix reversals act not on permutations but on strings over a fixed size alphabet.  determine the minimum number of prefix reversals required to sort binary and ternary strings, with polynomial-time algorithms for these sorting problems as a result; demonstrate that computing the minimum prefix reversal distance beten two binary strings is NP-hard; give an exact expression for the prefix reversal diameter of binary strings; and give bounds on the prefix reversal diameter of ternary strings.  also consider a aker form of sorting called grouping (of identical symbols) and give polynomial-time algorithms for optimally grouping binary and ternary strings. A number of intriguing open problems are also discussed."}]