Star　networks　play　an　essential　role　in　designing　parallel　and　distributed　systems.　With　the　massive　growth　of　faulty　edges　and　the　widespread　applications　of　the　longest　paths　and　cycles,　it　is　crucial　to　embed　the　longest　fault-free　paths　and　cycles　in　edge-faulty　networks.　However,　the　traditional　fault　model　allows　a　concentrated　distribution　of　faulty　edges　and　thus　can　only　tolerate　faults　that　depend　on　the　minimum　degree　of　the　network　vertices.　This　paper　introduces　an　improved　fault　model　called　the　partitioned　fault　model,　which　is　an　emerging　assessment　model　for　fault　tolerance.　Based　on　this　model,　we　first　explore　the　longest　fault-free　paths　and　cycles　by　proving　the　edge　fault-tolerant　Hamiltonian　laceability,　edge　fault-tolerant　strongly　Hamiltonian　laceability,　and　edge　fault-tolerant　Hamiltonicity　in　the　$n$-dimensional　star　network　$Sn$.　Furthermore,　based　on　the　theoretical　proof,　we　give　an　$O(nN)$　algorithm　to　construct　the　longest　fault-free　paths　in　star　networks　based　on　the　partitioned　fault　model,　where　$N$　is　the　number　of　vertices　in　$Sn$.　We　also　make　comparisons　to　show　that　our　result　of　edge　fault　tolerance　has　exponentially　improved　other　known　results.　IEEE