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 ...

This course covers advanced topics in approximation algorithms for NP-hard problems, including combinatorial algorithms and LP-based algorithms for set cover, k-cut, k-center, feedback vertex set, ...

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 ...

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

This paper proposes an algorithm that automatically translates the "continuum approximation" (CA) recipes for location problems into discrete designs. It applies to terminal systems, but can also be ...

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 ...

June 5, 2024 — In a new paper in Science Advances on May 29, researchers at JPMorgan Chase, the U.S. Department of Energy’s (DOE) Argonne National Laboratory and Quantinuum have demonstrated clear ...