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 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 ...

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 ...

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 ...

We demonstrate its applicability by considering the min-cost flow problem, by giving a novel algorithm for linear programming over unimodular spaces, and by providing a different proof that for ...

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.