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If a problem is weakly NP-hard, then it does not have a weakly polynomial time algorithm (polynomial in the number of integers and the number of bits in the largest integer), but it may have a pseudopolynomial time algorithm (polynomial in the number of integers and the magnitude of the largest integer). An example is the 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.
Pseudo-polynomial time algorithms (4 P) Pages in category "Weakly NP-complete problems" ... Subset sum 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.
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.
Is graph canonization polynomial time equivalent to the graph isomorphism problem? Can leaf powers and k-leaf powers be recognized in polynomial time? Can parity games be solved in polynomial time? Can the rotation distance between two binary trees be computed in polynomial time? Can graphs of bounded clique-width be recognized in polynomial ...