To Index or Not to Index: Optimizing Exact Maximum Inner Product Search

Exact Maximum Inner Product Search (MIPS) is an important task that is widely pertinent to recommender systems and high-dimensional similarity search. The brute-force approach to solving exact MIPS is computationally expensive, thus spurring recent development of novel indexes and pruning techniques for this task. In this paper, we show that a hardware-efficient brute-force approach, blocked matrix multiply (BMM), can outperform the state-of-the-art MIPS solvers by over an order of magnitude, for some -- but not all -- inputs. In this paper, we also present a novel MIPS solution, MAXIMUS, that takes advantage of hardware efficiency and pruning of the search space. Like BMM, MAXIMUS is faster than other solvers by up to an order of magnitude, but again only for some inputs. Since no single solution offers the best runtime performance for all inputs, we introduce a new data-dependent optimizer, OPTIMUS, that selects online with minimal overhead the best MIPS solver for a given input. Together, OPTIMUS and MAXIMUS outperform state-of-the-art MIPS solvers by 3.2$\times$ on average, and up to 10.9$\times$, on widely studied MIPS datasets.Comment: 12 pages, 8 figures, 2 table

F:\IJCAS\sept 2010 ijcas\3Aasth

[2] Principle: In isocratic HPLC the analyte is forced through a column of the stationary phase (usually a tube packed with small round particles with a certain surface chemistry) by pumping a liquid (mobile phase) at high pressure through the column. The sample to be analyzed is introduced in a small volume to the stream of mobile phase and is retarded by specific chemical or physical interactions with the stationary phase as it traverses the length of the column. Nature of the analyte, stationary phase and mobile phase composition accounts for the retardation. The time at which a specific analyte elutes (comes out of the end of the column) is called the retention time and is considered a reasonably unique identifying characteristic of a given analyte. Pressure increases the linear velocity (speed) of the component providing it less time to diffuse within the column, which leads to improved resolution in the resulting chromatogram. Any miscible combinations of water or various organic liquids (the most common are methanol and acetonitrile) serves as the solvent system. Water may contain buffers or salts to assist in the separation of the analyte components, or compounds such as Trifluoroacetic acid which acts as an ion pairing agent In spite of being considered somewhat mature, new developments in HPLC still continue. There have been improvements in column construction, packing material design, bonded phase chemistry and formats. In addition to this, new phases have extended the pH range (high and low), providing it more versatility. [3] Instrumentation: The heart of a HPLC system is the column. The column contains the particle that contains the Stationary phase. Pump forces the mobile phase to pass through the column and injector injects the mixture to be separated into the flowing mobile phase. Molecules that are adsorbed maximum by stationary phase are eluted slowest through the column, whereas the molecules which are High Performance Liquid Chromatography (HPLC) is a highly improved form of column chromatography in which instead of a solvent being allowed to drip through a column under gravity, it is forced through under high pressures of up to 400 atmospheres(500-5000 p.s.i). The sensitivity and range of the technique depends on the choice of column and on the efficiency of the overall system. Column technology has seen great developments over the years. The transition from large porous particles and pellicular materials to small porous particles occurred in the early 1970s, when micro particulate silica gel (10 -mm dp) came into light and appropriate packing methods were developed. Monolithic columns are a promising alternative to packed columns in the future but much of the research is yet to be done. The use of CAPILLARY COLUMNS (4 mm) has increased in recent years, in part because small-diameter columns use much less solvent and provide higher sensitivity. While speaking of the future of packaging development, silica gel with chemically bonded phases will be around for a long time. The field is a promising one with great scope for research and development