Emerging　crowdsensing　applications　imposed　a　new　barrier　coverage　problem　called　min-max　sink-based　linear　barrier　coverage　(min-max　SLBC).　In　the　problem,　we　are　given　a　group　of　sinks　distributed　on　a　plane,　each　of　which　can　disseminate　an　infinite　number　of　nonuniform　mobile　sensors.　The　aim　is　to　cover　a　given　linear　barrier　using　mobile　sensors　disseminated　from　the　sinks,　such　that　the　maximum　energy　consumed　by　sensor　movement　is　minimized.　We　devise　a　polynomial　algorithm　for　min-max　SLBC　with　nonuniform　sensors,　despite　the　sensor-based　linear　barrier　coverage　counterpart　of　the　problem　was　proven　strongly　NP-hard.　To　this　end,　we　first　present　a　polynomial　-time　algorithm,　namely　Separated　Target　Coverage　Algorithm　(STCA),　for　optimally　solving　the　discretized　version　of　min-max　SLBC.　Then　we　devise　the　exact　algorithm　called　Segment　Collaborative-Coverage　Algorithm　(SCCA)　for　the　continuous　version　of　min-max　SLBC,　by　improving　an　approximate　solution　computed　by　STCA　to　eventually　obtain　an　arguably　optimal　solution.　Lastly,　numerical　experiments　are　carried　out　to　validate　the　efficiency　and　effectiveness　of　SCCA　via　comparing　with　other　baselines　including　the　state-of-art　algorithms.　(c)　2022　Elsevier　B.V.　All　rights　reserved.