In　this　work,　we　investigate　the　problem　of　maximizing　nonmonotone　DR-submodular　function　(possibly　negative)　subject　to　cardinality　constraints　on　an　integer　lattice　space.　We　propose　a　M-Threshold　Decrease　Algorithm　that　uses　a　compensation　constant..　from　a　special　decomposition　h(x)　=　f(x)　-　g(x),　which　achieves　a　1　-　e(-delta)　-　epsilon　approximation　guarantee.　To　ensure　that　the　algorithm　ends　in　finite　time,　the　supremum　of　delta　is　delta(epsilon)　=　epsilon　max(s　is　an　element　of　Omega)　h(chi(s)vertical　bar　0)/2k　max(s　is　an　element　of　Omega)　g(chi(s)vertical　bar　0)+epsilon　max(s　is　an　element　of　Omega)　h(chi(s)　0).　If　max(s　is　an　element　of　Omega)　h(chi(s　vertical　bar　vertical　bar)0)　＞　2k　max(s　is　an　element　of　Omega)　g(chi(s)vertical　bar　0),　there　exists　epsilon*　=　arg　max(epsilon　is　an　element　of(0,1))　1　-　e(-delta(epsilon))　-　epsilon　such　that　1　-　e(-delta(epsilon)*())　-　epsilon*　＞　0.　This　implies　that　there　is　a　valid　delta　such　that　1　-　e(-delta)　＞　0.　To　accelerate　the　algorithm,　we　employ　a　random　subset　to　replace　the　ground　set　and　propose　a　Random　M-Threshold　Decrease　Algorithm,　where　delta(epsilon)　=　epsilon　r　max(s　is　an　element　of　Omega)　h(chi(s)vertical　bar　0)/2k　max(s　is　an　element　of　Omega)　g(chi(s)vertical　bar　0)+[k(n-r)+epsilon　r]　max(s　is　an　element　of　Omega)　h(chi(s　vertical　bar)0)　with　being　the　size　of　the　random　subset　and　n　being　the　size　of　the　ground　set.　Furthermore,　we　demonstrate　that,　based　on　the　DR-ratio　gamma(d)　and　the　DS　decomposition,　the　M-Threshold　Decrease　Algorithm　is　also　suitable　for　solving　the　monotone　non-DR-submodular　maximization　problem,　achieving　a　1　-　e-(gamma　d　delta)　-　O(epsilon)　approximation　guarantee.　Because　gamma(d)　is　a　challenging　metric　to　calculate,　we　refine　the　M-Threshold　Decrease　Algorithm,　which　can　return　an　estimate　of　gamma(d).　To　the　best　of　our　knowledge,　this　is　the　first　time　that　a　single　factor　approximation　ratio　has　been　proposed　for　the　nonmonotone　DR-submodular　maximization　problem　(possibly　negative)　subject　to　cardinality　constraints.