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The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of n {\displaystyle n} items numbered from 1 up to n {\displaystyle n} , each with a weight w i {\displaystyle w_{i}} and a value v i {\displaystyle v_{i}} , along with a maximum weight capacity ...
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
Another related problem is the bottleneck travelling salesman problem: Find a Hamiltonian cycle in a weighted graph with the minimal weight of the weightiest edge. A real-world example is avoiding narrow streets with big buses. [15] The problem is of considerable practical importance, apart from evident transportation and logistics areas.
A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time many-one reduction from L to H. [1]: 80 Another definition is to require that there be a polynomial-time reduction from an NP-complete problem G to H.
The bin packing problem can also be seen as a special case of the cutting stock problem. When the number of bins is restricted to 1 and each item is characterized by both a volume and a value, the problem of maximizing the value of items that can fit in the bin is known as the knapsack problem .
In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O(2 p(n)) time, where p(n) is a polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. A number of problems are known to be EXPTIME-complete.
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in ...
Global Fashion Group (GFG) was established in 2014 through a consolidation of fashion e-commerce regional companies backed by Kinnevik and Rocket Internet.Its regional companies Dafiti, Lamoda, The Iconic, Zalora and Jabong (later sold) were founded in 2011 and 2012.