http:^^www.cs.washington.edu^homes^brendan^mkbm^mkbm.html

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Date: Tue, 10 Dec 1996 21:21:42 GMTServer: NCSA/1.4.2Content-type: text/htmlLast-modified: Mon, 04 Sep 1995 19:47:16 GMTContent-length: 3084<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN"><!Converted with LaTeX2HTML 95.1 (Fri Jan 20 1995) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds ><HEAD><TITLE>Upper and Lower Bounds on Constructing Alphabetic Binary Trees</TITLE></HEAD><BODY><meta name="description" value="Upper and Lower Bounds on Constructing Alphabetic Binary Trees"><meta name="keywords" value="mkbm"><meta name="resource-type" value="document"><meta name="distribution" value="global"><P> <BR> <HR><A NAME=tex2html3 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="next" SRC="http://www.cs.washington.edu/homes/speed/figs/next_motif.gif"></A>   <IMG ALIGN=BOTTOM ALT="up" SRC="http://www.cs.washington.edu/homes/speed/figs/up_motif_gr.gif">   <IMG ALIGN=BOTTOM ALT="previous" SRC="http://www.cs.washington.edu/homes/speed/figs/previous_motif_gr.gif">         <BR><B> Next:</B> <A NAME=tex2html4 HREF="node1.html"> Overview</A><BR> <HR> <P> <H1>Upper and Lower Bounds on Constructing Alphabetic Binary Trees</H1><P><STRONG>MARIA KLAWE<A NAME=tex2html1 HREF="footnode.html#3"><IMG ALIGN=BOTTOM ALT="gif" SRC="http://www.cs.washington.edu/homes/speed/figs/foot_motif.gif"></A> andBRENDAN MUMEY<A NAME=tex2html2 HREF="footnode.html#4"><IMG ALIGN=BOTTOM ALT="gif" SRC="http://www.cs.washington.edu/homes/speed/figs/foot_motif.gif"></A></STRONG><P><P><STRONG></STRONG><P><P><H3>Abstract:</H3><EM>This paper studies the long-standing open question of whetheroptimal alphabetic binary trees can be constructed in <IMG  ALIGN=MIDDLE ALT="" SRC="img3.gif"> time.  We show that a class of techniques for finding optimal alphabetic trees which includes all current methods yielding <IMG  ALIGN=MIDDLE ALT="" SRC="img4.gif"> time algorithms are at leastas hard as sorting in whatever model of computation is used.We also give <IMG  ALIGN=MIDDLE ALT="" SRC="img5.gif"> time algorithms for the case where all the inputweights are within a constant factor of one another and whenthey are exponentially separated.</EM><P><BR> <HR><UL> <LI> <A NAME=tex2html5 HREF="node1.html#SECTION00010000000000000000"> Overview</A><LI> <A NAME=tex2html6 HREF="node2.html#SECTION00020000000000000000"> Current Methods</A><LI> <A NAME=tex2html7 HREF="node3.html#SECTION00030000000000000000"> Region-based Methods</A><LI> <A NAME=tex2html8 HREF="node4.html#SECTION00040000000000000000"> The Constant Factor Case</A><LI> <A NAME=tex2html9 HREF="node5.html#SECTION00050000000000000000"> Hardness Results</A><UL> <LI> <A NAME=tex2html10 HREF="node6.html#SECTION00051000000000000000"> Finding the lmcp tree</A><LI> <A NAME=tex2html11 HREF="node7.html#SECTION00052000000000000000"> Region-based Methods</A></UL> <LI> <A NAME=tex2html12 HREF="node8.html#SECTION00060000000000000000"> Conclusions</A><LI> <A NAME=tex2html13 HREF="node9.html#SECTION00070000000000000000">References</A><LI> <A NAME=tex2html14 HREF="node10.html#SECTION00080000000000000000">   About this document ... </A></UL><BR> <HR><P><ADDRESS><I>Brendan Mumey <BR>Mon Sep  4 11:52:47 PDT 1995</I></ADDRESS></BODY>

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