For　a　given　graph　G　with　non-negative　integral　edge　length,　a　pair　of　distinct　vertices　s　and　t,　and　a　given　positive　integer　delta,　the　k　partial　edge-disjoint　shortest　path　(kPESP)　problem　aims　to　compute　k　shortest　st-paths　among　which　there　are　at　most　d　edges　shared　by　at　least　two　paths.　In　this　paper,　we　first　present　an　exact　algorithm　with　a　runtime　O(mnlog((1+m/n))　n　+　delta　n(2))　for　kPESP　with　k　=　2.　Then　observing　the　algorithm　can　not　be　extended　for　general　k,　we　propose　another　algorithm　with　a　runtime　O(delta　2(k)n(k+1))　in　DAGs　based　on　graph　transformation.　In　addition,　we　show　the　algorithm　can　be　extended　to　kPESP　with　an　extra　edge　congestion　constraint　that　each　edge　can　be　shared　by　at　most　C　paths　for　a　given　integer　C　＜=　k.