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An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. [122]
[10] For many classes of graphs, a maximum weight independent set may be found in polynomial time. Famous examples are claw-free graphs, [11] P 5-free graphs [12] and perfect graphs. [13] For chordal graphs, a maximum weight independent set can be found in linear time. [14]
The second list is based on the 2024 edition of The Military Balance, published by the International Institute for Strategic Studies (IISS) using average market exchange rates. [2] The third list is a user-generated list of the highest military budgets of the current year, compiled from various sources.
The English Wikipedia, with over 6.9 million articles, remains the largest of the editions, which together comprise more than 64 million articles and attract more than 1.5 billion unique device visits and 13 million edits per month (about 5 edits per second on average) as of April 2024.
Focusing on sales and trading, ex-DVA, revenue improved 10% year over year to 4.1 billion. This is the first time we've recorded more than 4 billion in our Q4 results, and it included Q4 records ...
[1] [2] In a series of papers, Grünbaum broadened the accepted definition of a polyhedron, discovering many new regular polyhedra. At the close of the 20th century these latter ideas merged with other work on incidence complexes to create the modern idea of an abstract polyhedron (as an abstract 3-polytope), notably presented by McMullen and ...
India was the world's second-largest textile exporter after China in the 2013 calendar year. [ 313 ] Averaging an economic growth rate of 7.5% for several years prior to 2007, [ 304 ] India has more than doubled its hourly wage rates during the first decade of the 21st century. [ 314 ]
The number of legal positions in chess is estimated to be (4.59 ± 0.38) × 10 44 with a 95% confidence level, [144] with a game-tree complexity of approximately 10 123. The game-tree complexity of chess was first calculated by Claude Shannon as 10 120 , a number known as the Shannon number . [ 145 ]