Coalition　formation　is　a　key　topic　in　multi-agent　systems.　One　may　prefer　a　coalition　structure　that　maximizes　the　sum　of　the　values　of　the　coalitions,　but　often　the　number　of　coalition　structures　is　too　large　to　allow　exhaustive　search　for　the　optimal　one.　Furthermore,　finding　the　optimal　coalition　structure　is　NP-hard　and　even　finding　a　sub-optimal　solution　requires　searching　an　exponential　number　of　solutions.　But　then,　can　the　coalition　structure　found　via　a　partial　search　be　guaranteed　to　be　within　a　bound　from　optimum?　Sandholm　et　al.　show　that　it　suffices　to　search　the　lowest　two　levels　of　the　coalition　structure　graph　in　order　to　establish　a　worst-case　bound　Kin).　Dang　et　al.　present　an　algorithm　which　is　obviously　faster　than　that　of　Sandholm　et　al,　which　is　the　best　result　known　so　far.　Against　this　background,　the　relations　among　coalition　structures　are　analyzed　in　depth　and　a　novel　anytime　algorithm　based　on　cardinality　structure　is　presented,　which　only　has　to　take　a　step　further　and　search　those　coalition　structures　whose　cardinality　structure　is　in　the　CCS　(n,　b).　Consequently,　the　algorithms　reported　are　obviously　better　than　that　of　Sandholm　et　al.　(up　to　1035　times　faster　when　n=100,　K=2)　and　Dang　et　al.　(up　to　1018　times　faster　when　n=l00,　K=3).