01 fractional programming problem (and Dinkelbach dichotomy algorithm)

link

Pre-skills

• Dichotomous thinking
• Shortest path algorithm
• Some mathematical brain cells?

Model 1 issue
basic 01 fractional programming problem
given n-tuple (value _i , cost _i ), value _i choose the value obtained in this tuple (non-negative), cost _i choose to pay the cost of this tuple (non-negative), provided X _I (X _I ∈ {0,1} represents the dyadic ii selected from the group and not selected, maximum (minimum) of the formula

Let me talk to maximize the following

Solution

dichotomy

Set r a maximum of r * ,