Tree search is a widely used fundamental algorithm. Modern processors provide tremendous computing power by integrating multiple cores, each with a vector processing unit. This paper reviews some studies on exploiting...Tree search is a widely used fundamental algorithm. Modern processors provide tremendous computing power by integrating multiple cores, each with a vector processing unit. This paper reviews some studies on exploiting single instruction multiple date （SIMD） capacity of processors to improve the performance of tree search, and proposes several improvement methods on reported SIMD tree search algorithms. Based on blocking tree structure, blocking for memory alignment and dynamic blocking prefetch are proposed to optimize the overhead of memory access. Furthermore, as a way of non-linear loop unrolling, the search branch unwinding shows that the number of branches can exceed the data width of SIMD instructions in the SIMD search algorithm. The experiments suggest that blocking optimized SIMD tree search algorithm can achieve 1.6 times response speed faster than the un-optimized algorithm.展开更多
We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random var...We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X_n, Y_n and Z_n are all asymptotically normal as n→∞by applying the contraction method.展开更多
基金Project supported by the Shanghai Leading Academic Discipline Project(Grant No.J50103)the Graduate Student Innovation Foundation of Shanghai University(Grant No.SHUCX112167)
文摘Tree search is a widely used fundamental algorithm. Modern processors provide tremendous computing power by integrating multiple cores, each with a vector processing unit. This paper reviews some studies on exploiting single instruction multiple date （SIMD） capacity of processors to improve the performance of tree search, and proposes several improvement methods on reported SIMD tree search algorithms. Based on blocking tree structure, blocking for memory alignment and dynamic blocking prefetch are proposed to optimize the overhead of memory access. Furthermore, as a way of non-linear loop unrolling, the search branch unwinding shows that the number of branches can exceed the data width of SIMD instructions in the SIMD search algorithm. The experiments suggest that blocking optimized SIMD tree search algorithm can achieve 1.6 times response speed faster than the un-optimized algorithm.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10671188)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KJCX3-SYW-S02)the Special Foundation of University of Science and Technology of China
文摘We consider three random variables X_n, Y_n and Z_n, which represent the numbers of the nodes with 0, 1, and 2 children, in the binary search trees of size n. The expectation and variance of the three above random variables are got, and it is also shown that X_n, Y_n and Z_n are all asymptotically normal as n→∞by applying the contraction method.
