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Consider the following problem, Non-Uniform Bin Packing: the input is a list of bin sizes and item sizes and we want to know if we can put all the items in the bins so no bin is overflowing. This problem is clearly in NP : an assignment of items to bins is of polynomial size with respect to the input, and we can check in polynomial time if none ...
The goal is to pack the items into bins such that each bin can hold any subset of items of total size at most 1, so as to minimize the number of bins used. The problem that I am struggling with is that I read that unless P = NP P = N P, it is not possible for a polynomial-time algorithm to compute a solution to this problem with a number of ...
For the relaxed bin packing, I should say that, sometimes you can relax/ignore some of the conditions in your problem. For example, in bin packing problem, one strict condition is that you should put each item into one bin and you cannot split one item into multiple bins. One may allow each item to be split into multiple bins (now this problem ...
2. I'm trying to devise an algorithm to solve the bin packing problem with conflicts (sometimes referred to as BPPC, or BPC). The problem is defined as follows: consider a set V V of n n items, where each item i i has an associated positive weight wi w i, and n n identical bins of capacity C C. In addition, there is an undirected graph G = (V ...
More simply put: Is bin-packing still NP-Complete if you allow for items to be separated into pieces, but there is a "penalty" for having more pieces in each bin, where you're forced to place a "filler" between each piece in a bin?
$\begingroup$ Well you could be asking for a more direct conversion, and/or a human explanation about their relationship, as the reductions given for one NP-complete problem to another can be multi-step (conversion to multiple intermediate problems) and lose a lot of easily "explainable" information.
The decision version of the Bin packing problem involves deciding whether a certain number of bins (for example, 9) is optimal. If your hypothetical polynomial-time greedy algorithm finded a solution for 9 bins and failed to find a solution for 8 bins, then the answer for the decision problem would definitely be yes, and no otherwise.
Here are the definitions for the traditional bin packing problem (BPP) and the flexible bin packing problem (F-BPP): Bin packing problem (BPP): Optimization problem: Given a set of n items and their corresponding volumes (the volume of each item is between 0 and 1), pack the n items into the minimum number of bins (each with capacity 1) such ...
In the bin packing with fragile objects (BPFO) problem one is given a set of objects $\{1,\ldots,n ...
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