Interval DP has form: . Some variants use depending on the problem.
Naive: states, choices per state = . Knuth's observation: if cost satisfies QI, then . This double bound limits where to search for . Summed over all states, total work becomes .
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
Core idea
Interval DP has form: . Some variants use depending on the problem.
Naive: states, choices per state = . Knuth's observation: if cost satisfies QI, then . This double bound limits where to search for . Summed over all states, total work becomes .