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1 parent f10aa29 commit 47173e0dacf75619ded699d33dc93a6a65c6e456 @dhruvbird dhruvbird committed May 18, 2012
Showing with 4 additions and 4 deletions.
  1. +4 −4 doc/pdpma.tex
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8 doc/pdpma.tex
@@ -52,16 +52,16 @@ \section{Introduction}
One of the deficiencies in the traditional PMA is that one element
insertions might trigger a rebalance of the entire array, which costs
$\Theta(N)$ element moves. In contrast, the amortized number of
-element moves, $\Theta(log^2 N)$, is not that bad. When we do such an
-insertion in a massive database, triggering a scan of the entire
+element moves, $\Theta(\log^2{N})$, is not that bad. When we do such
+an insertion in a massive database, triggering a scan of the entire
database is infeasible. We may not be able to (or want to) wait while
the data structure rebuilds itself. To overcome this deficiency,
following the work(s) of Bender, Cole, Demaine, Farach-Colton, and
Zito \cite{2-simplified-algorithms}, and Willard \cite{willard},
-Haodong Hu in his thesis \cite{haodong-thesis} \cite{adaptive-pma}
+Haodong Hu in his thesis \cite{haodong-thesis, adaptive-pma}
introduces a partially deamortized packed-memory array whose
insert/delete cost per update is at most
-$\mathcal{O}({\sqrt{N}log\,N})$. Even though Haodong Hu's pardially
+$\mathcal{O}({\sqrt{N}\log{N}})$. Even though Haodong Hu's pardially
deamortized PMA is considerably simpler than the fully deamortized one
introduced by Willard, it is still hard to implement.

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