# How to prove that there is no algorithm with worst-case running time better than this one?

I have the following data:

• A set $$V$$ of tasks, the starting time $$s_j$$ of each task and the duration $$p_j$$ of each task.

• A set $$K$$ of resource, each resource has an availability function $$R_{k}$$ that is piecewise constant.That is, for each $$t = 0, .., T-1$$, we precise $$R_{k}(t)$$ the number of units available at $$t$$. $$R_k$$ is an array of length $$T$$.

• Each task $$j$$ needs $$r_{j,k}$$ resources to be processed (it could be zero). This quantity needs to be available during all the processing time starting from $$s_j$$.

Here is my attempt to verify that the resource utilization at each $$t$$ is no larger than the availability function.

Algorithm