Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the rate-distortion relationship in the set of permutations endod with the Kendall    $\tau $   -metric and the Chebyshev metric (the    $\ell _\infty $   -metric).  is motivated by the application of permutation rate-distortion to the average-case and worst-case distortion analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall    $\tau $   -metric,  provide bounds for various distortion regimes, while for the Chebyshev metric,  present bounds that are valid for all distortions and are especially accurate for small distortions. In addition, for the Chebyshev metric,  provide a construction for covering codes.
['Farzad Farnoud Hassanzadeh', 'Moshe Schwartz', 'Jehoshua Bruck']
I am writing a research paper on a idea Bounds for Permutation Rate-Distortion
[{"from": "human", "value": "I am writing a research paper on a idea Bounds for Permutation Rate-Distortion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the rate-distortion relationship in the set of permutations endod with the Kendall    $\\tau $   -metric and the Chebyshev metric (the    $\\ell _\\infty $   -metric).  is motivated by the application of permutation rate-distortion to the average-case and worst-case distortion analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall    $\\tau $   -metric,  provide bounds for various distortion regimes, while for the Chebyshev metric,  present bounds that are valid for all distortions and are especially accurate for small distortions. In addition, for the Chebyshev metric,  provide a construction for covering codes."}]