Sandor Szabo and Bogdan Zavalnij

Abstract
In the paper we propose to convert NP-hard combinato-
rial optimization problems of packing, covering, and tiling
types into maximum or 𝑘-clique problems. The key step is
to come up with a tactically constructed auxiliary graph
whose maximum or 𝑘-cliques correspond to the sought com-
binatorial structure. As an example, we will consider the
problem of packing a given cube by copies of a brick. The
aim of the paper is two fold to illustrate the modeling power
and the feasibility of the clique approach. Since theoretical
tools are not readily available to study the effectiveness of
the solution of the resulting clique problems we will carry
out carefully conducted numerical experiments.