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Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
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.
The 900 hp (670 kW) V12 Winton 201-A-engined NC and NW series locomotives can be distinguished from the less powerful 600 hp (450 kW) SC and SW because, although the underframes are identical, the hood on the N series is longer, leaving only a small amount of room before the front walkway. Many, but not all, N series locomotives have a short ...
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No-penalty CDs vs. savings account: How to choose. For many retirees, combining a no-penalty CD and a savings account can offer the best of both worlds. Use a high-yield savings account for funds ...
Great Value's Cream Cheese won consistently high marks across all of our editors' tastings for its balance of sweetness, tartness, and saltiness.
Informally, an NP-complete problem is an NP problem that is at least as "tough" as any other problem in NP. NP-hard problems are those at least as hard as NP problems; i.e., all NP problems can be reduced (in polynomial time) to them. NP-hard problems need not be in NP; i.e., they need not have solutions verifiable in polynomial time.
(Reuters) - Shares of Google parent Alphabet rose about 5% on Tuesday after it unveiled a new generation chip that the company said helped overcome a key challenge in quantum computing.