Crowdsensing　is　becoming　a　hot　topic　because　of　its　advantages　in　the　field　of　smart　city.　In　crowdsensing,　task　allocation　is　a　primary　issue　which　determines　the　data　quality　and　the　cost　of　sensing　tasks.　In　this　paper,　on　the　basis　of　the　sweep　covering　theory,　a　novel　coverage　metric　called　＇t-sweep　k-coverage＇　is　defined,　and　two　symmetric　problems　are　formulated:　minimise　participant　set　under　fixed　coverage　rate　constraint　(MinP)　and　maximise　coverage　rate　under　participant　set　constraint　(MaxC).　Then　based　on　their　submodular　property,　two　task　allocation　methods　are　proposed,　namely　double　greedy　(dGreedy)　and　submodular　optimisation　(SMO).　The　two　methods　are　compared　with　the　baseline　method　linear　programming　(LP)　in　experiments.　The　results　show　that,　regardless　of　the　size　of　the　problems,　both　two　methods　can　obtain　the　appropriate　participant　set,　and　overcome　the　shortcomings　of　linear　programming.　Copyright　©　2020　Inderscience　Enterprises　Ltd.