>
What Is The 'Canary Mission' And Why Are US Officials Using It To Attack The First Amendment
Democrats Move to Sanction El Salvador For 'Gross Violations' of Human Rights...
Jeffrey Epstein's Brother Breaks Silence On Bombshell FBI Memo
FICO Stock Down More Than 10% This Week After FHFA Opens Door To VantageScore For Mortgages
Insulator Becomes Conducting Semiconductor And Could Make Superelastic Silicone Solar Panels
Slate Truck's Under $20,000 Price Tag Just Became A Political Casualty
Wisdom Teeth Contain Unique Stem Cell That Can Form Cartilage, Neurons, and Heart Tissue
Hay fever breakthrough: 'Molecular shield' blocks allergy trigger at the site
AI Getting Better at Medical Diagnosis
Tesla Starting Integration of XAI Grok With Cars in Week or So
Bifacial Solar Panels: Everything You NEED to Know Before You Buy
INVASION of the TOXIC FOOD DYES:
Let's Test a Mr Robot Attack on the New Thunderbird for Mobile
Facial Recognition - Another Expanding Wolf in Sheep's Clothing Technology
The salesman problem is this question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?". Having really good solutions for this class of problems means the US postal service, Fedex, UPS, airlines and the US military would save huge amounts of money. It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research.
Conventional digital computers, including supercomputers, are inadequate to solve these complex problems in practically permissible time as the number of candidate solutions they need to evaluate increases exponentially with the problem size. This is a combinatorial explosion. D-Wave Systems and others have created "Ising machines" and "quantum annealers," have been actively developed in recent years. There is complicated pre-processing to convert each task to the form they can handle and have a risk of presenting illegal solutions that do not meet some constraints and requests, resulting in major obstacles to the practical applications.
Approximation Algorithms
Various heuristics and approximation algorithms, which quickly yield good solutions, have been devised. These include the Multi-fragment algorithm. Modern methods can find solutions for extremely large problems (millions of cities) within a reasonable time which are with a high probability just 2–3% away from the optimal solution.
Exact algorithms
The most direct solution would be to try all permutations (ordered combinations) and see which one is cheapest (using brute-force search). The running time for this approach lies within a polynomial factor of {displaystyle O(n!)}O(n!), the factorial of the number of cities, so this solution becomes impractical even for only 20 cities.