Commit dbb01577 authored by Filip Stedronsky's avatar Filip Stedronsky
Browse files

Succinct: merge definitions into a list

parent adabac6b
......@@ -24,14 +24,17 @@ 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 with $s(n) \le OPT(n) + \O(1)$.}
\defn{A data structure is
\tightlist{o}
\:{\I implicit} when $s(n) \le OPT(n) + \O(1)$,
\:{\I succinct} when $s(n) \le OPT(n) + {\rm o}(OPT(n))$,
\:{\I compact} when $s(n) \le \O(OPT(n))$.
\endlist
}
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 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
length-$n$ sequence of numbers from range $[m]$ needs $\O(n (\log n + \log m))$
......@@ -45,4 +48,5 @@ fast operations on these space-efficient data structures.
\section{Succinct representation of strings}
\endchapter
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment