Denna tjänst avvecklas 2026-01-19. Läs mer här (länk)

Denna tjänst avvecklas 2026-01-19. Läs mer här (länk)

MINIMUM WEIGHTED COMPLETION TIME SCHEDULING

• INSTANCE: Set T of tasks, number m of identical processors, for each task $t\in T$ a release time $r(t)\in Z^+$, a length $l(t)\in Z^+$, and a weight $w(t)\in Z^+$.

• SOLUTION: An m-processor schedule for T that obeys the resource constraints and the release times, i.e., a function $f : T \rightarrow N \times [1..m]$ such that, for all $u \geq 0$ and for each processor i, if S(u,i) is the set of tasks t for which $f(t)_{1} \leq u < f(t)_{1}+l(t)$ and $f(t)_{2}=i$, then $\vert S(u,i)\vert = 1$ and for each task t, $f(t)_{1} \geq r(t)$.

• MEASURE: The weighted sum of completion times, i.e. $\sum_{t\in T} w(t)(f(t)_1+l(t))$.

  
  

• Good News: Approximable within 2 [432].

• Comment: The preemptive case is also approximable within 2 [401]. Generalization to unrelated processors (where the length of a task also depends in the processor) is approximable within 2$+\varepsilon$ for any $\varepsilon >0$ for both nonpreemptive and preemptive scheduling [432]. Restriction (of the nonpreemptive case) where r(t)=0 for all t is approximable within 3/2 [433]. Generalization where there are precedence constraints on T that must be obeyed in the solution is approximable within 5.33 [96].

• Garey and Johnson: SS13