“…Though simple to define, such "grouping" problems often pose significant challenges in practical settings because it is not always easy to judge whether the imposed constraints can be satisfied. Indeed many such problems including those concerning graph partitioning (Hertz et al, 2008;Isomoto et al, 1993;Jensen and Toft, 1994;Nakano1 et al, 1995), school and university timetabling (Lewis, 2008;McCollum et al, 2010), sports fixture scheduling (de Werra, 1988;Kendall et al, 2010;Rasmussen and Trick, 2008), load balancing (Falkenauer, 1998), and frequency assignment (Aardel et al, 2002;Valenzuela, 2001), are known to be NP-hard (Garey and Johnson, 1979;Karp, 1972), implying that we cannot hope to establish polynomially bounded algorithms for solving them in the general sense.…”