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An example is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition problem.
An example is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition problem.
Download as PDF; Printable version; ... Pseudo-polynomial time algorithms (4 P) Pages in category "Weakly NP-complete problems"
A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. A problem is NP-complete if it is both in NP and NP-hard. The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do.
An example is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition problem.
That is, assuming a solution for H takes 1 unit time, H ' s solution can be used to solve L in polynomial time. [1] [2] As a consequence, finding a polynomial time algorithm to solve a single NP-hard problem would give polynomial time algorithms for all the problems in the complexity class NP.
It runs in polynomial time on inputs that are in SUBSET-SUM if and only if P = NP: // Algorithm that accepts the NP-complete language SUBSET-SUM. // // this is a polynomial-time algorithm if and only if P = NP. // // "Polynomial-time" means it returns "yes" in polynomial time when // the answer should be "yes", and runs forever when it is "no".
Such problems arise in approximation algorithms; a famous example is the directed Steiner tree problem, for which there is a quasi-polynomial time approximation algorithm achieving an approximation factor of () (n being the number of vertices), but showing the existence of such a polynomial time algorithm is an open problem.