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The KK algorithms essentially solve the [[configuration linear program]]:<blockquote><math>\text{minimize}~~\mathbf{1}\cdot \mathbf{x}~~~\text{s.t.}~~ A \mathbf{x}\geq \mathbf{n}~~~\text{and}~~ \mathbf{x}\geq 0~~~\text{and}~~ \mathbf{x}~\text{is an integer}~</math>.</blockquote>Here, '''''A''''' is a matrix with ''m'' rows. Each column of '''''A''''' represents a feasible ''configuration'' - a multiset of item-sizes, such that the sum of all these sizes is at most ''B''. The set of configurations is ''C''. '''x''' is a vector of size ''C.'' Each element ''x<sub>c</sub>'' of '''x''' represents the number of times configuration ''c'' is used.
* ''Example'':<ref name=":22">{{Cite web|last=Claire Mathieu|title=Approximation Algorithms Part I, Week 3: bin packing|url=https://www.coursera.org/learn/approximation-algorithms-part-1/home/week/3
There are two main difficulties in solving this problem. First, it is an [[Integer programming|integer linear program]], which is computationally hard to solve. Second, the number of variables is ''C'' - the number of configurations, which may be enormous. The KK algorithms cope with these difficulties using several techniques, some of which were already introduced by de-la-Vega and Lueker.<ref name=":0" /> Here is a high-level description of the algorithm (where <math>I</math> is the original instance):
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