Energy　efficiency　is　a　critical　issue　that　attracts　numerous　interest　of　many　researchers　in　wireless　mobile　sensor　networks.　Emerging　IoT　applications　have　brought　the　MinSum　Sink-based　Linear　Barrier　Coverage　(MinSum　SLBC)　problem　which　aims　to　use　sink-based　mobile　sensors　(such　as　drones)　to　cover　a　line　barrier　(such　as　borders　possibly　for　monitoring　illegal　intrusion).　In　the　scenario,　all　the　sensors　are　initially　located　at　k　sink　stations,　while　the　aim　is　to　find　the　final　positions　of　the　sensors　on　the　line　barrier,　such　that　the　line　barrier　is　completely　covered　and　the　total　movement　of　the　sensors　is　minimized.　In　this　paper,　we　first　study　geometry　properties　of　an　optimal　solution　of　MinSum　SLBC,　and　reveal　that　an　optimal　solution　of　MinSum　SLBC　actually　consist　of　intersecting　segments　of　tangent　sensors.　Then,　we　devise　a　segmentation　algorithm　for　computing　a　near-optimal　position　of　each　segment　that　is　possibly　part　of　the　optimum.　Lastly,　by　selecting　segments　consisting　of　tangent　sensors　via　transforming　to　the　shortest　path　problem,　we　eventually　derive　a　factor-　(1　+　Ε)　approximation　algorithm　with　a　time　complexity　O(k2(log2rΕ+logk),　where　Ε＞　0　is　any　given　positive　real　number.　©　2021,　Springer　Nature　Switzerland　AG.