Questions tagged [succinct-data-structures]
15 questions
4
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1 answer
Looking for a succinct dynamic sorted dictionary
I was digging through research articles to find a data structure that solves the dynamic sorted dictionary problem (representing any subset $S$ of a universe $U = \{0, \ldots, u\}$ with member/predecessor/successor queries), but sadly I was able to…
John Doe the Righteous
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4
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2 answers
Succinct data structure to return occurences of letters until an index
I want to try and use a succinct type data structure in order to find the amount of occurences of a letter $C$ in a string $S$ until a given index $I$.
Assume we have a string $S$ of length $n$ over the alphabet $\Sigma = \{1,2,3,\ldots,n\}$. I want…
Ori Refael
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3
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1 answer
Compact mapping from an involuted set
Let $S$ be a set (say positive integers $\leq$ N) and $f$ an involution ($f$ is bijective, $f\cdot f=id$, e.g. xor with a constant). $g$ is a idempotent mapping choosing an arbitrary representative element in each $f$ mapped pairs. For example…
Piezoid
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3
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Generalization of XOR Linked Lists
Are there any results generalizing XOR Linked Lists to other types of data structures?
For example, just like an XOR Linked List requires two pointers and can iterate a 1 dimensional list, I can imagine a two dimensional linked list where nodes are…
Realz Slaw
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3
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1 answer
Is this an example of a natural, strictly NP-intermediate language (assuming EXP ≠ NEXP)?
In the wikipedia page for the NP-intermediate complexity class, the following observation is made:
Under the assumption that P ≠ NP, Ladner explicitly constructs a problem in NPI, although this problem is artificial and otherwise uninteresting. It…
Federico
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2
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0 answers
$y$-Fast Tries: Why not partition into groups of $\Theta(\log^2 M)$ elements?
The $y$-fast trie is a data structure for storing a sorted collection of $n$ integers from the range $[0, M)$. It builds on the $x$-fast trie, which also stores elements in this range.
The space usage of an $x$-fast trie is $O(n \log M)$ words. To…
templatetypedef
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2
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1 answer
Information-theoretic lower bound for succinct string dictionary of the Unicode Name property
Background
The literature on succinct data structures refers often to the “information-theoretic lower bound” of encoding data, i.e., the minimum number of bits needed to store the data – a concept related to information-theory entropy. For…
jschoi
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2
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0 answers
Storing relations space efficiently?
Let $f$ be a binary relation defined on set $S$, which contains numbers from $1$ to $n$. It is also given that number of $|\text{Img}(f)| \le k$. I want to store the function $f$ such in way such that space required is minimum.
I am trying to store…
user94342
1
vote
1 answer
Heap-like notation of a BST (BFT bit-vectors) for succinct representation
I'm researching the topic of succinct tree representations right now and came across this presentation. On slide 17 there is an example of heap-like notation of a BST (using BFT bit-vectors) and the author claims that the amount of bits needed to…
ddnomad
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1
vote
1 answer
Subintervals during backward search of a BWT
A Burrows-Wheeler Transform (BWT) can be used to find the suffix array intervals for a pattern $P$ by issuing $p=|P|$ paired $rank$ queries
\begin{align}
s^\prime &= C[P[i]] + rank(s-1, P[i]) + 1 \\
e^\prime &= C[P[i]] + rank(e,…
alan
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0
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1 answer
How many bits do the pointers take?
So I am covering succinct trees, and in the lecture, it mentioned that "An n-node tree takes 2n pointers or 2n lg n bits (can be easily reduced to n lg n + O(n) bits). First, question is why 2nlgn bits, and how we can reduce it to nlgn?
kjkjkjkjkj
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Succinct array datastracture
Is it true that there is no known succinct data structure that has integer array (vector) functionality? Desirable operations would be:
append O(1)
access(i) - returns i-th item O(1)
iterate(i..j) - i.e. iterate from i to j efficiently O(j-i)
The…
mcmayer
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0
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1 answer
How to analyze the amortized running time of indexed linked list operations using potential method?
I have implemented an indexed linked list that runs (under mild assumptions) all single-element operations in $\mathcal{O}(\sqrt{n})$ time. The description is here and Java implementation is here.
It’s clear to me that the running time is linear in…
coderodde
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What are the graph classes which takes logarithmic space in $|V|$ in circuit representation?
The $\text{SCR}$ representation of a graph $G=(V,E)$ is $C_{G}$ id the following conditions hold:
$C_{G}$ is a combinatorial circuit with memory.
$C_{G}$ has two inputs of length $n$ bits.
$C_{G}$ has $r$ gates, where $r = \mathcal{O}(n^{k})$ for…
user102006
-3
votes
1 answer
Exponential amount of information in polynomial size? Impossible!
I'm reading A note on succinct representations of graphs by Papadimitriou and Yannakakis. Let me quote the following paragraph on page 183:
Formula $F$ has a highly regular structure. It has $|x|$ clauses stating that the input to the computation…
Zirui Wang
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