The travelling salesman problem (TSP) remains one of the most challenging NP‐hard problems in combinatorial optimisation, with significant implications for logistics, network design and route ...

Next, we will study algorithms for NP-hard problems whose solutions are guaranteed to be within some approximation factor of the best possible solutions. Such algorithms are often quite efficient and ...

The course will introduce the underlying computational concepts (polynomial-time computation and NP-completeness); introduce canonical problem models including graph problems and formula ...

We consider two generalizations of the fixed job schedule problem, obtained by imposing a bound on the spread-time or on the working time of each processor. These NP-hard problems, studied by the ...

Since cutting stock problems are well known to be NP-hard, it is prohibitive to obtain optimal solutions. We develop approximation algorithms for different purposes: quick response algorithms for ...

The Stanford researchers apply Grover’s algorithm to the number partitioning problem by encoding each possible partition of the integer list as a quantum state. They also formulate an oracle that can ...

D-Wave demonstrates performance advantage in quantum simulation The algorithm the researchers use to demonstrate this is known as an interactive proof protocol. Here, one component of the experimental ...

It turns out that the optimization belongs to a set of mathematical problems that are called NP-hard, making them extremely difficult to calculate as the length of the chain goes up.

The course will introduce the underlying computational concepts (polynomial-time computation and NP-completeness); introduce canonical problem models including graph problems and formula ...