  We give a simple algorithm for decremental graph connectivity that handles
edge deletions in worst-case time $O(k \log n)$ and connectivity queries in
$O(\log k)$, where $k$ is the number of edges deleted so far, and uses
worst-case space $O(m^2)$. We use this to give an algorithm for $k$-edge
witness (``does the removal of a given set of $k$ edges disconnect two vertices
$u,v$?'') with worst-case time $O(k^2 \log n)$ and space $O(k^2 n^2)$. For $k =
o(\sqrt{n})$ these improve the worst-case $O(\sqrt{n})$ bound for deletion due
to Eppstein et al. We also give a decremental connectivity algorithm using
$O(n^2 \log n / \log \log n)$ space, whose time complexity depends on the
toughness and independence number of the input graph. Finally, we show how to
construct a distributed data structure for \kvw by giving a labeling scheme.
This is the first data structure for \kvw that can efficiently distributed
without just giving each vertex a copy of the whole structure. Its complexity
depends on being able to construct a linear layout with good properties.
