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 ...

Understand how approximation algorithms compute solutions that are guaranteed to be within some constant factor of the optimal solution. Develop a basic understanding of how linear and integer ...

Such algorithms find approximate (slightly suboptimal) solutions to optimization problems in polynomial time. Unlike heuristics, approximation algorithms have provable performance guarantees: they ...

The algorithm we propose, IES, gives an approximate solution to the LHD problem regardless of its dimension and size with a theoretical performance guarantee. We introduce two upper bounds for the ...

Michel Gendreau, Gilbert Laporte, Alain Hertz, An Approximation Algorithm for the Traveling Salesman Problem with Backhauls, Operations Research, Vol. 45, No. 4 (Jul ...

Such algorithms find approximate (slightly suboptimal) solutions to optimization problems in polynomial time. Unlike heuristics, approximation algorithms have provable performance guarantees: they ...

Although efficient in a strictly theoretical sense (i.e., in the sense of taking polynomial versus exponential time), this algorithm for the permanent is not practical. Indeed, to date, no practical ...