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However, it is a long-standing ( since 1975 ) open problem to improve the Christofides approximation factor of 1. 5 for general metric TSP to a smaller constant.
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However, the system is designed, ingeniously and hopefully, so that no one man could initiate a thermonuclear war.
However, there is always the possibility that chance will make demands the dancers find impossible to execute.
However, it is important to trace the philosophy of the French Revolution to its sources to understand the common democratic origin of individualism and socialism and the influence of the latter on the former.
However, it was not of innocence in general that I was speaking, but of perhaps the frailest and surely the least important side of it which is innocence in romantic love.
However, neither of these two cities is on the desired July 1 to June 30 fiscal year.
However, there is a more profound consideration to this proposed merger than profit and loss.
However, if their United States income is not subject to the withholding of tax on wages, their returns are due June 15, 1962, if they use a calendar year, or the 15th day of the 6th month after the close of their fiscal year.
However, its modern one-story layout is designed to increase our production capacity, permit more efficient manufacturing, and substantially reduce current repair and maintenance costs.
However, because this vulnerability is mutual, it is to the advantage of neither side to destroy the opponent's cities, at least so long as the opponent has nuclear weapons with which to effect reprisal.
However, there is a minimum of legislative restriction on boating.
However, it is essential that the various mathematical symbols used in the equations be understood so that the mathematical processes can be done properly and in their correct order.
However, the use of tripods is not allowed.
However, there is also much to be gained by making use of the abilities of the local people who are available and interested in recreation.
However, that is not all he has to do.
However one looks at it, therefore, I'd say that your horoscope for this autumn is the reverse of rosy.
However, a major factor in binding dirt is the attraction between surfaces that goes under the name of Van der Waal's forces.
However, the conversion from mass to size is unreliable, since many photographic meteors give evidence of a fluffy, loosely bound meteorite structure with densities as low as Af.
However, as a field measurement, it is open to question.
However, this artery is known to be a nutrient vessel with a distribution primarily to the proximal airways and supportive tissues of the lung.
However, if there is no additional complex of singular lines, the order of the image regulus of a pencil is precisely Af.
However, the factor of physical isolation is not a static situation.
However, any such suggestion accounts for only some of the difficulties in hearing tone, or in developing a realistic attitude about tone, but not for the analytic difficulties that occur even when tone is meticulously recorded.
However, there always is some limit to the numbers who will spend the time and effort to acquire training.
However and long-standing
However it has had long-standing close relations with its other neighbors Afghanistan, Iran and China, extensive security and economic interests in the Persian Gulf and wide-ranging bilateral relations with the United States and other Western countries.
However, Yamato Japan and Baekje had been long-standing and very close allies.
However, nowadays Agrigento is one of the poorest towns in Italy on a per capita income basis and has a long-standing problem with organised crime, particularly involving the Mafia and the smuggling of illegal drugs.
However, at Court the match was not so popular among the elder members of court due to the long-standing tensions between Austria and France, which had only recently been mollified.
However, on October 28, 2008, McKenna said that he would not be seeking the leadership, saying " Although I have been deeply moved by expressions of support for me from across the country, I have not been persuaded to change my long-standing resolve to exit public life for good ," and
The existence of the AKS primality test finally settled this long-standing question and placed PRIMES in P. However, PRIMES is not known to be P-complete, and it is not known whether it lies in classes lying inside P such as NC or L.
However, the local Métis people who already inhabited the area had long-standing ties with the NWC, and refused to accept Selkirk's control over the area.
However there were long-standing rivalries between the locals of both towns and in July that year violence broke out when an order was given to remove the paupers to Amersham.
However, the Swan River Colony ( Western Australia ) accepted transportation from England and Ireland in 1851, to resolve a long-standing labour shortage.
However, the silver was eventually sold to pay off long-standing debts incurred by the Neue Rheinische Zeitung.
However, a long-standing problem for the association has been that it is not always taken seriously, and instead is dismissed by many as a " bunch of drugged-out hippies ".
However, it abandoned its long-standing activist stance and allowed school history to be submerged within the ill-defined, antidisciplinary domain of " social studies.
However, he had a long-standing conflict with his coach, Don Nelson.
However, American craftsmen were unencumbered by the various long-standing allegiances of European craft guilds that sometimes stifled advances in technology out of economic self-interest.
However, there has been academic commentary to the effect the learned judge reached a conclusion that cannot be reconciled with the international cases or long-standing English case law.
However, with the advent of New Winkies, coupled with the now flat and dry pitches, teams with good kicks are becoming gradually more and more likely to convert a behind, making the long-standing ropes defensive strategy less useful.
However, Surakiart's supporters contended that he spearheaded Thailand's " prosper thy neighbor " policy of regional economic coordination and that his quiet diplomatic style had helped resolve numerous long-standing regional disputes.
However, an attempt on Modern Air's part to pass on a further increase in its fuel surcharge to Berliner Flugring for the planned 1974 /' 75 winter flying programme resulted in the tour operator's refusal to renew its long-standing charter contract with the airline.
However, a permanent home proved difficult to find and it was not until late 1988 and the closure of the local Odeon cinema by Rank Leisure that the theatre's long-standing Artistic Director, Alan Ayckbourn, found a suitable venue.
However, most stars are not given proper names, relying on either long-standing traditional names ( usually from the Arabic ), or catalogue numbers.
However, at the 2012 municipal elections, the Labour Party ousted long-standing Conservative councillor ( and the then Leader of the Conservative Group at the Town Hall ) Keith Bland in a landslide victory.
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