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datovky
ds2-notes
Commits
adabac6b
Commit
adabac6b
authored
Aug 28, 2021
by
Filip Stedronsky
Browse files
Succinct: use new formalism in definitions
parent
66e3e642
Changes
1
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Side-by-side
fs-succinct/succinct.tex
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adabac6b
...
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@@ -24,13 +24,13 @@ The information-theoretical optimum is $OPT(n) := \lceil\log |X(n)|\rceil$
Now we can define three classes of data structures based on their fine-grained space
efficiency:
\defn
{
An
{
\I
implicit data structure
}
is one
that uses at most
$
OPT
(
n
)
+
\O
(
1
)
$
bits of space
.
}
\defn
{
An
{
\I
implicit data structure
}
is one
with
$
s
(
n
)
\le
OPT
(
n
)
+
\O
(
1
)
$
.
}
A typical implicit data structure contains just its elements in some order and nothing more.
Examples include sorted arrays and heaps.
\defn
{
A
{
\I
succinct data structure
}
is one
that uses at most
$
OPT
(
n
)
+
{
\rm
o
}
(
OPT
(
n
))
$
bits of space
.
}
\defn
{
A
{
\I
compact data structure
}
is one
that uses at most
$
\O
(
OPT
(
n
))
$
bits of space
.
}
\defn
{
A
{
\I
succinct data structure
}
is one
with
$
s
(
n
)
\le
OPT
(
n
)
+
{
\rm
o
}
(
OPT
(
n
))
$
.
}
\defn
{
A
{
\I
compact data structure
}
is one
with
$
s
(
n
)
\le
\O
(
OPT
(
n
))
$
.
}
Note that some linear-space data structures are not even compact -- because we
are counting bits now, not words. For example, a linked list representing a
...
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