Although the problem is not known to be in NC, parallel algorithms with time superior to the Euclidean algorithm exist ; the best known deterministic algorithm is by Chor and Goldreich, which ( in the CRCW-PRAM model ) can solve the problem in O ( n / log n ) time with n < sup > 1 + ε </ sup > processors.

Although they found it superior in most ways, it was still at an early stage of development ; the Marines chose the technically inferior but mature M16.

Although inferior courts are bound in theory by superior court precedent, in practice judges may sometimes attempt to evade precedent by distinguishing it on spurious grounds.

Although there is nothing intrinsic about RP that marks it as superior to any other variety, sociolinguistic factors have given Received Pronunciation particular prestige in parts of Britain.

Although the latter was the most common type used in the past, cooks tend to be divided on whether carbon steel or cast iron woks are superior.

Although it was known that the Cardassians were supplying weapons to one side, Sisko's superior noted, " The Cardassians might involve themselves in other people's civil wars, but we don't.

Although Fang Zhimin's troops were soon destroyed, these movements surprised the Kuomintang, who were numerically superior to the Communists at the time and did not expect an attack on their fortified perimeter.

Although Charlotte Brontë's Jane Eyre was generally considered the best of the Brontë sisters ' works during most of the nineteenth century, many subsequent critics of Wuthering Heights argued that it was a superior achievement.

Although the single-cylinder Ossa had 20 horsepower less than its rivals, it was 45 pounds lighter and its monocoque frame was much stiffer than conventional motorcycle frames, giving it superior agility on the racetrack.

Although the Republicans heavily outnumbered their opponents and managed to push 12 kilometres inland, superior Nationalist air power mainly provided by Fascist Italy forced the Republicans to retreat and to leave the island completely by September 12.

" Although the majority of scholars continue to favor the Masoretic as a superior text, many other scholars have now adopted Kahle's thesis.

Although the young gentlemen technically were ratings, holding a rank below warrant officers at the mercy of the captain, as aspiring future commissioned officers they were considered socially superior and were often given a watch ( with authority over some warrant officers ) or a minor command.

Although Lincoln believed his plan was superior, he was relieved that McClellan finally agreed to begin moving, and reluctantly approved.

Although the 709 was a superior machine to its predecessor, the 704, it was being built and sold at the time that transistor circuitry was supplanting vacuum tube circuits.

Although some of the sources listed here treat only one kind of VaR as legitimate, most of the recent ones seem to agree that risk management VaR is superior for making short-term and tactical decisions today, while risk measurement VaR should be used for understanding the past, and making medium term and strategic decisions for the future.

Although he had endeavoured to restrain the King of Sardinia from his rash attack on the superior forces of Austria, he obtained for him a reduction of the penalty of defeat.

Although British leadership was found lacking, British infantry's superior discipline showed that however much French infantry had improved under Saxe's tutelage, France could not match the best that Britain could put in the field.

Although Steinitz became " world number one " by winning in the all-out attacking style that was common in the 1860s, he unveiled in 1873 a new positional style of play and demonstrated that it was superior to the previous style.

Although " How Sweet It Is ( To Be Loved By You )" surpassed it in two out of three charts, "( I'm a ) Road Runner " is regarded as a superior offering from Junior Walker & The All-Stars, one of three songs by the band ( along with " Way Back Home " and " Shotgun " included in 1999's Da Capo Press publication The heart of rock & soul: the 1001 greatest singles ever made.

Although thyristors are heavily used in megawatt scale rectification of AC to DC, in low and medium power ( from few tens of watts to few tens of kilowatts ) they have almost been replaced by other devices with superior switching characteristics like MOSFETs or IGBTs.

Although they possessed superior weaponry they were greatly outnumbered by ARBiH soldiers who were defending the city.

Although originally sold as a secret medicine, Warburg's Tincture was highly regarded by many eminent medical professionals who considered it as being superior to quinine ( e. g. Surgeon-General W. C. Maclean, Professor of Military Medicine at British Army Medical School, Netley ).

Although they are somewhat superior to straight-4s in terms of vibrations, they have largely fallen out of favor because they have two cylinder banks thus requiring twice as many camshafts as a straight-4 ( if an OHC rather than OHV or F-head configuration is used ) while the crankshaft is as complex to manufacture.

Although superior to the Prussian army that tried to prevent his advance, they were so poorly equipped that the advance did not get far and the campaign saw only minor engagements.

Although gold has an atomic number of 79, immediately after Rutherford's paper appeared in 1911 Antonius Van den Broek made the intuitive suggestion that atomic number is nuclear charge.

Although his paper was widely cited, a random selection of 60 of these citations revealed that 29 of the papers were direct rebuttals or criticisms of Jensen's arguments, 8 cited the paper as an " example of controversy ," 8 used it as a background reference.

Although most early codices were made of papyrus, papyrus was fragile and supplies from Egypt, the only place where papyrus grew and was made into paper, became scanty ; the more durable parchment and vellum gained favor, despite the cost.

Although recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave Coriolis, in connection with the theory of water wheels, Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

Although silk was a somewhat expensive medium to paint upon in the past, the invention of paper during the 1st century AD by the Han court eunuch Cai Lun provided not only a cheap and widespread medium for writing, but also a cheap and widespread medium for painting ( making it more accessible to the public ).

Although greatly improved and with many variations, the Fourdriner machine is the predominant means of paper production today.

The 2006 Senate Report on Pre-war Intelligence on Iraq stated that " Although DIA coordinated on CIA's Iraqi Support for Terrorism paper, DIA analysis preceding that assessment was more skeptical of the al-Libi reporting.

Although today Sophus Lie is rightfully recognized as the creator of the theory of continuous groups, a major stride in the development of their structure theory, which was to have a profound influence on subsequent development of mathematics, was made by Wilhelm Killing, who in 1888 published the first paper in a series entitled

Although Maxwell did not explicitly mention the sea of molecular vortices, his derivation of Ampère's circuital law was carried over from the 1861 paper and he used a dynamical approach involving rotational motion within the electromagnetic field which he likened to the action of flywheels.

Although the present-day concepts of literacy have much to do with the 15th century invention of the movable type printing press, it was not until the Industrial Revolution of the mid-19th century that paper and books became financially affordable to all classes of industrialized society.

Although acid-free paper has become more common, a large body of acidic paper still exists in books made after the 1850s because of its cheaper and simpler production methods.

" Although originally written as a joke by editor Martyn Cornell, the paper ran it.

Although its uses had transferred to parchment, papyrus therefore just overlapped with the use of paper in Europe, which began in the 11th century.

Although Chebyshev's paper did not prove the Prime Number Theorem, his estimates for π ( x ) were strong enough for him to prove Bertrand's postulate that there exists a prime number between n and 2n for any integer n ≥ 2.

Although no model or workable device was ever made, it is often seen as a link to the concept of punched paper for player piano rolls ( 1880s ), as well as Herman Hollerith's punch card tabulator ( used in the 1890 United States census ), a distant precursor of the modern computer.

Although some of the basic workings of the theory were proposed and identified by Mayr in 1954, historians of science generally recognize the 1972 paper by Niles Eldredge and Stephen Jay Gould as the foundational document of the new paleobiological research program.

Although I have much to write to you, I would rather not use paper and ink ; instead I hope to come to you and talk with you face to face, so that our joy may be complete.

Although the print version of the paper remains the largest local metropolitan newspaper in the United States, it is the third largest newspaper overall, behind The Wall Street Journal and USA Today, and its weekday circulation has fallen since 1990 ( as have other newspapers ) to fewer than one million copies daily.

Although its paper size is bigger, its style was copied from the British tabloids.

Although a typical plot might easily require a few thousand paper motions, back and forth, the paper doesn't slip.

Although the paper ran the editorial in the seventh place on the page, below even one on the newly invented " chainless bicycle ", its message was very moving to many people who read it.