Commit adabac6b authored by Filip Stedronsky's avatar Filip Stedronsky
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Succinct: use new formalism in definitions

parent 66e3e642
......@@ -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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