As　wireless　and　mobile　networks　are　getting　more　of　a　commonplace,　the　discovery　and　management　of　dynamic　networks　has　become　a　serious　issue..　Since　the　topology　of　wireless　and　mobile　networks　always　keeps　changing,　the　key　issue　of　topology　discovery　is　how　to　effectively　and　efficiently　perform　the　discovery　task　with　minimal　impact　to　normal　network　traffic.　In　this　paper　we　analyze　the　efficiency　of　some　current　topology　discovery　methods　used　both　in　wired　and　wireless　networks　and　show　that　they　are　not　very　efficient.　We　also　analyze　the　main　reason　and　present　a　new　method　called　BacktraceTree　to　improve　efficiency　of　topology　discovery.　The　BacktraceTree　first　backtraces　the　topology　tree　by　probing　the　destination　nodes　which　give　response　and　can　find　most　topology　nodes　and　links,　and　then　it　discovers　the　remainder　topology　by　analyzing　the　known　topology　features　and　probing　the　unresponding　destination　nodes.　We　describe　and　analyze　the　BacktraceTree　algorithm　and　compare　it　with　some　major　current　topology　discovery　methods.　Our　evaluation　shows　that　BacktraceTree　can　reduce　almost　70%　measurement　load　while　maintaining　the　coverage　of　router　interfaces　above　95%.　The　BacktraceTree　algorithm　can　dramatically　improve　topology　discovery　and　can　thus　meet　the　requirement　for　fast　topology　discovery　in　wireless　and　mobile　networks.　©　2008　IEEE.