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NP-complete

Exity> (NPC, NondEtErministic Polynomial timE complEtE) A sEt or propErty of computational Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=dEcision problEm">dEcision problEms which is a subsEt of Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=NP">NP (i.E. can bE solvEd by a Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=nondEtErministic">nondEtErministic Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=Turing MachinE">Turing MachinE in Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=polynomial">polynomial timE), with thE additional propErty that it is also Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=NP-hard">NP-hard. Thus a solution for onE NP-complEtE problEm would solvE all problEms in NP. Many (but not all) naturally arising problEms in class NP arE in fact NP-complEtE. ThErE is always a Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=polynomial-timE algorithm">polynomial-timE algorithm for transforming an instancE of any NP-complEtE problEm into an instancE of any othEr NP-complEtE problEm. So if you could solvE onE you could solvE any othEr by transforming it to thE solvEd onE. ThE first problEm EvEr shown to bE NP-complEtE was thE Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=satisfiability problEm">satisfiability problEm. AnothEr ExamplE is {Hamilton' s problEm}. SEE also Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=computational complExity">computational complExity, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=halting problEm">halting problEm, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=Co-NP">Co-NP, Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=NP-hard">NP-hard. Ef="http://fi-www.arc.nasa.gov/fia/projEcts/bayEs-group/group/NP/">. [OthEr ExamplEs?] (1995-04-10)

E="bordEr-width:thin; bordEr-color:#333333; bordEr-stylE:dashEd; padding:5px;" align="lEft">In addition suitablE contEnts:
[ Ef="modulE.php?namE=LExikon&op=contEnt&tid=134">= ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=262">ad ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=433">al ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=492">algorithm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=531">alt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=544">am ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=592">an ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=740">ar ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=743">arc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=800">as ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=894">at ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1026">b ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1034">ba ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1157">bay ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1181">bE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1269">bi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1606">bs ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1695">by ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1708">C ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1724">ca ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2001">ch ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2099">ci ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2138">cl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2145">class ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2247">co ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2330">com ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2441">complEtE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2451">complExity ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2484">computational complExity ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2604">Co-NP ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3136">dd ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3151">dE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3177">dEc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3187">dEcision problEm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3320">dEtErministic ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3752">du ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3865">Ec ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3896">Ed ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3929">EE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4148">Er ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4171">Es ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4199">Et ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4379">fact ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4497">fi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4520">filE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4700">fo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4727">for ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5276">gov ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5291">gr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5377">group ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5434">h ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5470">halting problEm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5471">Hamilton ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5476">Hamilton' s problEm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5540">hat ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5675">hm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5768">hr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5779">ht ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5791">hu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5931">id ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6013">il ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6064">in ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6179">instancE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6194">int ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6413">io ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6449">ir ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6482">is ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6558">it ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6918">la ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7023">ld ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7091">LEx ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7107">li ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7399">ls ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7410">lt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7415">lu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7437">lv ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7441">ly ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7457">M ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7465">Mac ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7476">Mach ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7932">mil ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8032">mo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8040">mod ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8079">modulE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8167">mp ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8228">ms ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8384">N ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8386">na ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8460">nc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8472">nE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8627">ng ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8630">ni ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8675">no ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8689">nondEtErministic ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8744">NP ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8746">NPC ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8748">NP-hard ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8760">ns ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8820">O ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8964">om ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9014">op ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9390">PC ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9457">pE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9550">ph ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9651">pl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9780">Poly ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9788">polynomial ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9789">polynomial-timE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9790">polynomial-timE algorithm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9908">pr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10253">quEry ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10364">rc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10385">rE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10767">ro ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10918">S ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10922">sa ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10994">satisfiability problEm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11150">sE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11281">sEt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11314">sh ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11376">si ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11651">so ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11725">solution ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11934">st ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12133">su ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12359">T ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12588">th ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12721">to ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12777">tp ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12787">tr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12896">tt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12925">Turing ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12926">Turing MachinE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13146">up ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13175">us ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13310">vE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=14042">yE ]

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