Say you have several queues A, B, ... Each queue has a length K_n. Each queue has a weight K_w. K_w adjusted such that \sumK_w=1 If k items are requested, a set of items from the tops of each relevant queue will be returned. K_c <= K_n items were chosen from queue K. Minimize \sum|kK_w-K_c|. << Jesus Christ that's it. How could I be so stupid. main(queueList, num) -> while (not have num) getNumOrAll(queueList[top], remaining) getNumOrAll(queue, num): Step 1: Make array of num*job.weight Step 2: "Remove" all num%1 from array, and count Step 3: "Sort" array by num. Step 4: Continue counting. Subtract one from each array member until at num. ^^ Not perfect Step 1: (Pre-)sort by job.data.length/job.weight. Step 2: Start at lowest, and pop all until job.data.length>job.normweight*num (decreasing num as popping and recalc job.normweight). Step 2.5: If empty, remove prio && jobs[prio]; return. Step 3: Then, pop job.normweight*num//1 elems from remaining, without num decrease or normweight recalc. But keep job.wacc = job.normweight*num%1 Step 4: Shallow copy job array, and sort by job.wacc. Step 5: Iterate through array (high->low), and subtract 1 until the length of output is num.