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<H1>(a,b)-tree</H1>
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(data structure)
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<strong>Definition:</strong>
A <a href="searchtree.html" tppabs="http://hissa.nist.gov/dads/HTML/searchtree.html"><em>search tree</em></a> with the restrictions that all <a href="leaf.html" tppabs="http://hissa.nist.gov/dads/HTML/leaf.html"><em>leaves</em></a> are at the same <a href="depth.html" tppabs="http://hissa.nist.gov/dads/HTML/depth.html"><em>depth</em></a> and all <a href="internalnode.html" tppabs="http://hissa.nist.gov/dads/HTML/internalnode.html"><em>internal nodes</em></a> have between a and b <a href="child.html" tppabs="http://hissa.nist.gov/dads/HTML/child.html"><em>children</em></a>. More formally a and b are integers such that 2 <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7 width=14 alt="less than or equal to"> a <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7 width=14 alt="less than or equal to"> (b+1)/2. If µ is an internal node with d children, the <a href="root.html" tppabs="http://hissa.nist.gov/dads/HTML/root.html"><em>root</em></a> has d <img src="geq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/geq.gif" border=0 height=7 width=14 alt="greater than or equal to"> 2, otherwise a <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7 width=14 alt="less than or equal to"> d <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7 width=14 alt="less than or equal to"> b.
<P><strong>See also</strong>
<a href="btree.html" tppabs="http://hissa.nist.gov/dads/HTML/btree.html"><em>B-tree</em></a>.
<P><em>Note:
From Algorithms and Theory of Computation Handbook, page 4-18, Copyright © 1999 by CRC Press LLC.</em>
<P>Author: <a href="terms.html#authorCRC-A" tppabs="http://hissa.nist.gov/dads/terms.html#authorCRC-A">CRC-A</a>
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Entry modified Thu Jun 17 09:56:40 1999.<BR>
HTML page formatted Wed Dec 22 09:34:38 1999.
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