From dbf98dde353bd81c70540dfbc0fc295fed781b57 Mon Sep 17 00:00:00 2001
From: Martin Mares <mj@ucw.cz>
Date: Fri, 21 Feb 2020 17:26:50 +0100
Subject: [PATCH] Hashing: Clarified theorem on complexity of Cuckoo hashing
---
06-hash/hash.tex | 6 ++++--
1 file changed, 4 insertions(+), 2 deletions(-)
diff --git a/06-hash/hash.tex b/06-hash/hash.tex
index 51ae449..3c85b2b 100644
--- a/06-hash/hash.tex
+++ b/06-hash/hash.tex
@@ -631,9 +631,11 @@ attempts (this is called insertion timeout), we give up and rehash everything
with new choice of $f$ and~$g$.
\theorem{
-Let $m\ge (2+\varepsilon)n$, insertion timeout be set to $\lceil 6\log n\rceil$ and
+Let $\varepsilon>0$ be a~fixed constant.
+Suppose that $m\ge (2+\varepsilon)n$, insertion timeout is set to $\lceil 6\log n\rceil$, and
$f$,~$g$ chosen at random from a~$\lceil 6\log n\rceil$-independent family.
-Then the expected time complexity of \alg{Insert} is $\O(1)$.
+Then the expected time complexity of \alg{Insert} is $\O(1)$, where the constant
+in~$\O$ depends on~$\varepsilon$.
}
\note{
--
GitLab