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 ...

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 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 ...

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

A string of improved approximation algorithms have since emerged, after computer scientists began looking at the problem with fresh eyes.

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 ...

In fact, this problem contains enough structure that computer scientists have developed a fast procedure (or algorithm) for it that bypasses the need for an exhaustive search.