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This algorithm can also be rewritten to use the Fast2Sum algorithm: [7] function KahanSum2(input) // Prepare the accumulator. var sum = 0.0 // A running compensation for lost low-order bits. var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around.
This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing nothing", with a cost of 0 for the taxi assigned to it. This reduces the problem to a balanced assignment problem, which can then be solved in the usual way and still give the best solution to the problem.
NC = P problem The P vs NP problem is a major unsolved question in computer science that asks whether every problem whose solution can be quickly verified by a computer (NP) can also be quickly solved by a computer (P). This question has profound implications for fields such as cryptography, algorithm design, and computational theory. [1]
Here, "quickly" means an algorithm that solves the task and runs in polynomial time (as opposed to, say, exponential time) exists, meaning the task completion time is bounded above by a polynomial function on the size of the input to the algorithm. The general class of questions that some algorithm can answer in polynomial time is "P" or "class ...
While it is easy to verify whether a given assignment renders the formula true, [1] no essentially faster method to find a satisfying assignment is known than to try all assignments in succession. Cook and Levin proved that each easy-to-verify problem can be solved as fast as SAT, which is hence NP-complete.
Other commonly used terms are assignment problem and one-sided matching. When agents already own houses (and may trade them with other agents), the problem is often called a housing market . [ 2 ] In house allocation problems, it is assumed that monetary transfers are not allowed; the variant in which monetary transfers are allowed is known as ...
The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution for H takes 1 unit time, H ' s solution can be used to solve L in polynomial time.