Kernekoncepter
The authors investigate the compression sensitivity of lex-parse for edit operations and alphabet ordering, providing tight upper and lower bounds for both scenarios.
Resumé
The content delves into the sensitivity analysis of lex-parse regarding edit operations and alphabet ordering. It explores various structures, such as Lyndon factorization and Fibonacci words, to characterize the behavior of lex-parse under different conditions. The study provides valuable insights into the robustness of lex-parse in handling small changes in input strings.
Statistik
MSsub(v, n), AOS(v, n) ∈ O(log n).
v(w2) ∈ O(b(w2) log(n/b(w2))) [21]
b(w2) ≤ 2b(w1) [1]
v(w, ≺) ∈ O(b(w) log(n/b(w)))
v(Fk, ≺):
⌈ k/2 ⌉ + 1 (if k is odd and a ≺ b)
4 (if k is odd and b ≺ a)
⌈ k/2 ⌉ + 1 (if k is even and a ≺ b)
4 (if k is even and b ≺ a)
Citater
"We investigate the compression sensitivity of lex-parse for two operations: single character edit and modification of alphabet ordering."
"Our analysis makes heavy use of properties of the Lyndon factorization of Fibonacci words to characterize the structure of lex-parse."
"The contributions are two-fold: analyzing sensitivity w.r.t. edit operations with logarithmic bounds and introducing alphabet-ordering sensitivity with tight upper and lower bounds."