WS 2007/2008 Fundamental Algorithms

1. (a,b)-Trees As we saw in the previous section, the efficiency of standard operations on binary search trees depends on the maximum tree height. Using height balancing, we ensure that trees cannot degenerate linearly but instead have logarithmic height. Let us extend this approach to more general trees. Motivation: assume tree nodes are stored in secondary storage (hard disk). Comparisons of keys of binary trees would be too time expensive due to mechanical positioning of the read-write head of the hard drive. Reading blocks of data (sectors, pages, etc.) is relatively fast provided the read-write head is positioned. Idea: store blocks of data in nodes of trees ! Advantages: faster access to the data and decreasing height of trees ! (a,b)-Trees have been invented by Rudolf Bayer and Edward M. McCreight (1976). 1. (a,b)-Trees As we saw in the previous section, the efficiency of standard operations on binary search trees depends on the maximum tree height. Using height balancing, we ensure that trees cannot degenerate linearly but instead have logarithmic height. Let us extend this approach to more general trees. Motivation: assume tree nodes are stored in secondary storage (hard disk). Comparisons of keys of binary trees would be too time expensive due to mechanical positioning of the read-write head of the hard drive. Reading blocks of data (sectors, pages, etc.) is relatively fast provided the read-write head is positioned. Idea: store blocks of data in nodes of trees ! Advantages: faster access to the data and decreasing height of trees ! (a,b)-Trees have been invented by Rudolf Bayer and Edward M. McCreight (1976). 1. (a,b)-Trees As we saw in the previous section, the efficiency of standard operations on binary search trees depends on the maximum tree height. Using height balancing, we ensure that trees cannot degenerate linearly but instead have logarithmic height. Let us extend this approach to more general trees. Motivation: assume tree nodes are stored in secondary storage (hard disk). Comparisons of keys of binary trees would be too time expensive due to mechanical positioning of the read-write head of the hard drive. Reading blocks of data (sectors, pages, etc.) is relatively fast provided the read-write head is positioned. Idea: store blocks of data in nodes of trees ! Advantages: faster access to the data and decreasing height of trees ! (a,b)-Trees have been invented by Rudolf Bayer and Edward M. McCreight (1976). 1. (a,b)-Trees As we …