Trajectories　contain　considerable　routing　information,　and　trajectory-based　routing　gains　the　attention　of　researchers　recently.　This　paper　argues　the　problem　of　searching　time　period　Longest　Frequent　Path(TPLFP).　The　TPLFP,　as　one　of　the　reasonable　alternative　Most　Frequent　Path　(MFP),　is　close　to　MFP　enough　and　maximizes　the　number　of　frequent　route　segments.　First,　we　define　TPLFP　formally.　To　acquire　accurate　path　frequencies,　we　describe　the　footmark,　the　footmark　graph　notations　and　design　the　Linear　Sketch　Footmark　Index　(LSFI)　to　speed　up　extracting　proper　footmark　and　constructing　related　footmark　graph.　Next,　we　develop　a　Best-First　search　algorithm　with　four　pruning　strategies.　Next,　we　give　an　advanced　footmark　graph　and　its　building　algorithm.　The　extensive　experiments　demonstrate　the　effectiveness　and　efficiency　of　our　index　schemes　and　algorithms,　which　can　find　TPLFP　results　in　expected　response　time.　©　2016　IEEE.