Behind this reply, and its many variations, is the ever-present budget problem all libraries must face, from the largest to the smallest.

To further highlight the difference between a problem and an instance, consider the following instance of the decision version of the traveling salesman problem: Is there a route of at most 2000 kilometres in length passing through all of Germany's 15 largest cities?

* Finding the largest complete graph is called the clique problem ( NP-complete ).

* Finding the largest edgeless induced subgraph, or independent set, called the independent set problem ( NP-complete ).

In 2005, Cook and others computed an optimal tour through a 33, 810-city instance given by a microchip layout problem, currently the largest solved TSPLIB instance.

The largest problem associated with the syndrome is severe obesity.

Difficulty in obtaining cell phone service from even the largest companies has been a problem for 94 % of the population in both rural and urban areas.

Graham's number, one of the largest numbers ever used in serious mathematical proof, is an upper bound for a problem related to Ramsey theory.

In Austria, Vienna has the largest number of reported trafficking cases, although trafficking is also a problem in urban centers such as Graz, Linz, Salzburg, and Innsbruck.

As an island in the 1830s, East Boston's largest problem was transportation.

The isoperimetric problem is to determine a plane figure of the largest possible area whose boundary has a specified length.

Although it is considered the largest cemetery in Latin America, the most serious problem at the cemetery is that it has run out of space.

Other AI laboratories ( of which the largest were Stanford, Carnegie Mellon University and the University of Edinburgh ) focussed on logic and formal problem solving as a basis for AI.

Tuberculosis is a major public health problem in China, which has the world's second largest tuberculosis epidemic ( after India ).

The largest problem is illegal settlements.

120 figures in Pierre de Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120.

The largest problem with the yasak system was that Russian governors were prone to corruption because they received no salary.

Other optimization problems on spanning trees have also been studied, including the maximum spanning tree, the minimum tree that spans at least k vertices, the minimum spanning tree with at most k edges per vertex ( Degree-Constrained Spanning Tree ), the spanning tree with the largest number of leaves ( closely related to the smallest connected dominating set ), the spanning tree with the fewest leaves ( closely related to the Hamiltonian path problem ), the minimum diameter spanning tree, and the minimum dilation spanning tree.

The largest value of the constant K can be obtained by solving the optimization problem

use this observation as part of an approximation algorithm for the problem of finding square labels of the largest possible size for a given set of points, with the constraint that each label has one of its corners on the point that it labels.

Similar questions have been studied with various other subgraphs H instead of K < sub > 3 </ sub >; for instance, the Zarankiewicz problem concerns the largest graph that does not contain a fixed complete bipartite graph as a subgraph.

We also have a problem, if, the largest prime divisor of the order of the Jacobian, is equal to the characteristic of By a different injective map we could then consider the DLP in the additive group instead of DLP on the Jacobian.

Both Alfred Harcourt and Donald Brace had written him enthusiastic praise of Elmer Gantry ( any changes could be made in proof, which was already coming from the printer ) and they had ordered 140,000 copies -- the largest first printing of any book in history.

Carson City could now advertise itself as one of America's largest state capitals with its of city limits.

Ō-daiko means " big fat drum ", but within any group, it describes the largest drum in an ensemble, which could mean in diameter or in diameter.

Greenland is believed by some geologists to have some of the world ’ s largest remaining oil resources: in 2001, the U. S. Geological Survey found that the waters off north-eastern Greenland ( north and south of the arctic circle ) could contain up to of oil and, in 2010, the British petrochemical company Cairns Oil reported " the first firm indications " of commercially viable oil deposits.

In pure mathematics, the magnitude of a googolplex could be related to other forms of large-number notation such as tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation, though neither googol nor googolplex are anywhere near the largest representable or even specifically named numbers.

" Antioch, a coastal city in northern Syria and the third largest in the Roman world, is often mentioned as this later home of the Matthean community, but it could have been any large city in the eastern Mediterranean with large Jewish and Christian populations, and recent research points towards a location near Galilee or Judea.

This quickly escalated into one of the largest search operations in Australian history, but no trace of Holt could be found.

In January 2010, the Kabul office of New Ansari Exchange, Afghanistan's largest hawala money transfer business, was shuttered following a raid by the Sensitive Investigative Unit, the country's national anti-political corruption vetted and trained by the US Drug Enforcement Administration ( DEA ), allegedly because this company could be involved in laundering profits from the illicit opium trade and moving the cash earned by Taliban through extortion and drug trafficking.

Isidore of Miletus and Anthemius of Tralles originally planned on a main hall of the Hagia Sophia that measured 230 feet by 250 feet, making it the largest church in Constantinople, but the original dome was nearly 20 feet lower than it was constructed, “ Justinian suppressed these riots and took the opportunity of marking his victory by erecting in 532-7 the new Hagia Sophia, one of the largest, most lavish, and most expensive buildings of all time .” Although Isidore of Miletus and Anthemius of Tralles were not formally educated in architecture, they were scientists that could organize the logistics of drawing thousands of laborers and unprecedented loads of rare raw materials from around the Roman Empire to create the Hagia Sophia for Emperor Justinian I.

In June 2012, two metal detectorists announced that they had uncovered what could be Europe's largest hoard of Iron Age Celtic coins, and which may be worth up to £ 10 M, after a search spanning 30 years.

This would bring the German fleet to a strength where it could contemplate challenging France or Russia, but would remain clearly inferior to the world's largest fleet, the Royal Navy.

At its peak, the stand could hold 28, 000 spectators and was one of the largest single-tier stands in the world.

Many stadia in England had stands named after Spion Kop, but Anfield's was the largest of them at the time ; it could hold more supporters than some entire football grounds.

In a review of pterosaur size estimates published in 2010, researchers Mark Witton and Mike Habib demonstrated that the latter, largest estimates are almost certainly incorrect given the total volume of a Pteranodon body, and could only be correct if the animal " was principally aluminium.

By 2008, more than 815, 000 vessels had passed through the canal, many of them much larger than the original planners could have envisioned ; the largest ships that can transit the canal today are called Panamax.

This postulate is necessary because it allows one to conclude that for a system at equilibrium, the thermodynamic state ( macrostate ) which could result from the largest number of microstates is also the most probable macrostate of the system.

It is regularly debated which could be considered the largest species of eagle.

# The largest available energy source could be a 500 kilowatt nuclear fission reactor.

Wildlife experts, however, argue the largest crocodile so far found in the Bhitarkanika was almost long, which could be traced from the skull preserved by the Kanika royal family.

Members of the Electoral College could only vote for president ; each elector could vote for two candidates, and the person who received the second largest number of votes during the balloting became vice-president.

Throughout most of the war, AK could be considered one of the three largest resistance movements in the war.

For example, Norman Davies wrote " Armia Krajowa ( Home Army ), the AK, which could fairly claim to be the largest of European resistance "; Gregor Dallas wrote " Home Army ( Armia Krajowa or AK ) in late 1943 numbered around 400000, making it the largest resistance organization in Europe "; Mark Wyman wrote " Armia Krajowa was considered the largest underground resistance unit in wartime Europe ".