From 7a1505027f33d78a777d21432a5f1aa33b2a006c Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Wed, 2 Apr 2008 17:24:58 +0200 Subject: [PATCH] Varia. --- macros.tex | 1 + opt.tex | 9 +++++++-- 2 files changed, 8 insertions(+), 2 deletions(-) diff --git a/macros.tex b/macros.tex index f70ca7f..850c162 100644 --- a/macros.tex +++ b/macros.tex @@ -53,6 +53,7 @@ \def\poly{\mathop{\rm poly}} \def\E{{\bb E}} \def\crpt{\mathop{\Uparrow}} +\def\C{{\cal C}} \def\brk{\hfil\break} diff --git a/opt.tex b/opt.tex index 32477d9..6ba150d 100644 --- a/opt.tex +++ b/opt.tex @@ -531,8 +531,6 @@ suffices to decrease~$\varepsilon$ twice. \section{Robust contractions} -\def\C{{\cal C}} - Having the soft heaps at hand, we would like to use them in a~conventional MST algorithm in place of a~usual heap. The most efficient specimen of a~heap-based algorithm we have seen so far is the Iterated Jarn\'\i{}k's algorithm (\ref{itjar}). @@ -749,4 +747,11 @@ time there. The rest of the algorithm spends $\O(m)$ time on the other operation and $\O(n)$ on identifying the live vertices. \qed +%-------------------------------------------------------------------------------- + +\section{An optimal algorithm} + + + + \endpart -- 2.39.5