Emerging　wireless　and　mobile　applications,　such　as　border　intrusion　detection　with　station-based　drones,　brought　a　new　barrier　coverage　problem　of　using　sink-based　mobile　sensors　to　cover　a　given　line　barrier　with　minimum　energy　consumption.　In　this　paper,　we　focus　on　the　uniform　sink-based　line　barrier　coverage　(SLBC)　problem,　in　which　we　are　given　a　line　barrier　and　k　sink　stations　distributed　on　the　plane　which　can　emit　an　infinite　number　of　sensors　with　an　identical　sensing　radius.　The　problem　aims　to　find　their　final　positions　on　the　barrier　for　the　sensors　emitted　by　the　stations,　such　that　the　total　moving　distance　of　the　sensors　is　minimized　and　each　point　of　the　barrier　is　within　the　sensing　area　of　at　least　one　sensor.　We　first　observe　the　geometric　structure　of　an　optimal　solution　that　any　optimal　solution　can　be　considered　as　a　set　of　intersecting　tangent　(disk)　segments,　where　a　tangent　(disk)　segment　is　a　sequence　of　tangent　disks.　Then,　we　devise　an　algorithm　to　calculate　all　possible　tangent　(disk)　segments　and　another　algorithm　to　calculate　the　near-optimal　positions　for　each　of　such　segments.　After　computing　all　tangent　(disk)　segments　and　their　near-optimal　positions,　an　algorithm　is　proposed　to　transform　uniform　SLBC　into　an　instance　of　the　shortest　path　problem.　It　is　shown　the　whole　algorithm　deserves　a　runtime　O(k2log⁡[Formula　presented])　and　consumes　at　most　ε　more　movement　than　an　optimal　solution,　where　ε　is　any　given　positive　real　number,　and　r　and　k　are　the　sensor　radius　and　the　number　of　sink　stations,　respectively.　©　2022