X-Git-Url: http://mj.ucw.cz/gitweb/?a=blobdiff_plain;f=dyn.tex;h=f07103ac08cc19f4d596c73cca1c8d1aee0545b5;hb=3ce379fec86d6348c80aa1d8c77fb64a0dbada13;hp=c0d97e6bc2f1e7e907dff4f371802eb840e61cfc;hpb=55c1a7d3c5c439a7475393dba7a1bef73e4f583e;p=saga.git diff --git a/dyn.tex b/dyn.tex index c0d97e6..f07103a 100644 --- a/dyn.tex +++ b/dyn.tex @@ -410,7 +410,7 @@ anyway.) } At the beginning, the graph contains no edges, so both invariants are trivially -satistifed. Newly inserted edges can enter level~0, which cannot break I1 nor~I2. +satisfied. Newly inserted edges can enter level~0, which cannot break I1 nor~I2. When we delete a~tree edge at level~$\ell$, we split a~tree~$T$ of~$F_\ell$ to two trees $T_1$ and~$T_2$. Without loss of generality, let us assume that $T_1$ is the @@ -516,7 +516,7 @@ to fit our needs, so we omit the details. %-------------------------------------------------------------------------------- -\section{Dynamic spanning forests} +\section{Dynamic spanning forests}\id{dynmstsect}% Let us turn our attention back to the dynamic MSF now. Most of the early algorithms for dynamic connectivity also imply $\O(n^\varepsilon)$