So far we have dealt mostly with the worst-case complexity of problems. We might also wonder aobut the average-case complexity of a problem, namely, how difficult the problem is to solve for an instance chosen randomly from some distribution. It may be the case for a certain problem that hard instances exist but are extremely rare. Many reductions use very specifically constructed problems, so ...

We improve a connection of the worst-case complexity and the average-case complexity of some well-known lattice problems. This fascinating connection was rst discovered by Ajtai 1] in 1996. We improve the exponent of this connection from 8 to 3:5 + .

We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on " generic-case complexity " we show that if a finitely generated group G has the word problem solv-able in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group,...

We prove a connection of the worst-case complexity to the average-case complexity based on the Closest Vector Problem (CVP) for lattices. Assume that there is an efficient algorithm which can solve approximately a random instance of CVP, with a non-trivial success probability, for lattices under a certain natural distribution, we show that one can approximately solve several lattice problems (i...

imagine you have traveled to an unfamiliar city. before you start your daily tour around the city, you need to know a good route. in network theory (nt), this is the traveling salesman problem (tsp). a dynamic programming algorithm is often used for solving this problem. however, when the road network of the city is very complicated and dense, which is usually the case, it will take too long fo...

the purpose of this study was to determine the clinical significance of changes in the plasma  adiponectin  concentration  in  patients  with  bronchial  asthma  and  to  test  the association between the single nucleotide polymorphisms (snps) rs2241766 and rs1501299 in the adipoq gene and bronchial asthma in the chinese li population.we selected 120 cases and 120 controls, and plasma adiponect...

kindler syndrome (ks) is a rare, autosomal recessive genodermatosis characterized by skin blistering and photosensitivity in infancy, progressive poikiloderma, and diffuse cutaneous atrophy. it affects the skin, mucous membranes, and oral cavity and is caused by mutations in the kind1 gene on 20p12.3. the first case of ks associated with periodontitis was reported in 1996, and have been infrequ...

lumbar hernias (lh) accounts for less than 1.5% of total hernia incidence. it can occur in two separate triangular areas of the flank. about 300 cases have been reported in the literature. here, we report a 55-year old man with acute painful left side flank mass and final diagnosis of lh. the mass was appeared about three hours before admission and his pain was slight at first but became more s...