Search results
Results From The WOW.Com Content Network
In computational complexity theory, a numeric algorithm runs in pseudo-polynomial time if its running time is a polynomial in the numeric value of the input (the largest integer present in the input)—but not necessarily in the length of the input (the number of bits required to represent it), which is the case for polynomial time algorithms.
This algorithm runs in time O(K N), where N is the number of elements in the input set and K is the sum of elements in the input set. The algorithm can be extended to the k -way multi-partitioning problem, but then takes O ( n ( k − 1) m k − 1 ) memory where m is the largest number in the input, making it impractical even for k = 3 unless ...
Pages in category "Pseudo-polynomial time algorithms" The following 4 pages are in this category, out of 4 total. This list may not reflect recent changes. K.
Although the partition problem is NP-complete, there is a pseudo-polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. For this reason, it has been called "the easiest hard problem".
SSP can be solved in pseudo-polynomial time using dynamic programming. Suppose we have the following sequence of elements in an instance: , …, We define a state as a pair (i, s) of integers. This state represents the fact that
There is a pseudo-polynomial time algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine, described below. Many cases that arise in practice, and "random instances" from some distributions, can nonetheless be solved exactly.
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.
In computational complexity theory, a pseudo-polynomial transformation is a function which maps instances of one strongly NP-complete problem into another and is computable in pseudo-polynomial time. [ 1 ]