# Questions tagged [ds.data-structures]

Properties and applications of data structures, such as space lower bounds, or time complexity of insertion and deletion of objects.

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### Encoding of nodes in Binary Decision Diagrams

A straightforward implementation of Binary Decision Diagrams (BDDs) typically requires 12 bytes per node, with an additional 4 bytes commonly used for auxiliary data. Each node is encoded as a 4-tuple ...
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### Why LOUDS is considered succinct coding?

LOUDS encoding is widely cited as succinct, e.g., in the papers, in Github repos, etc. It is straightforward that LOUDS takes 2n bits for encoding an ordered tree ...
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1 vote
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### Is it possible to encode the structure of a binary cardinal tree with n nodes using only n bits?

By binary cardinal tree, I mean a tree with degree 2. The question confuses me because I know LOUDS/DFUDS can encode binary trees with 2n bits; however, this paper claims that it is possible to encode ...
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### Data structure whose name starts with the letter “N”?

I’m working on an “ABC” poster of data structures, with one data structure per letter of the alphabet. (It’s intended as decor for a child’s room.) I teach an advanced data structures course and it ...
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### $\log^\star n$ is somewhat common in runtimes. Does the superroot ever make an appearance?

Many algorithms and data structures have iterated logarithms ($\log^\star n$) in their runtimes. This function is the discrete inverse of tetration, in that $$\log_a^\star (a \uparrow \uparrow b) = b$$...
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### Recent advances in computer science since 2010?

Since I left school (early 2010s) a couple of recently developed techniques were widely adopted by the industry. For example, Asymmetric numeral systems for compression (e.g. Ubuntu ships with ...
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### Deamortization of basic COLA (Cache oblivious lookahead array)

I am reading the paper titled Cache Oblivious Streaming B-trees. I am trying to understand the deamortization technique used for basic COLA. The paper says that for every level k, for deamortization, ...
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### What are examples of recent relatively simple 'toolbox algorithms'?

Taking an introduction to algorithms course, one encounters quicksort, minimal spanning tree, Dijkstra, Ford–Fulkerson algorithm etc. There are also several relatively standard data structures, such ...
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### kd-tree optimality for orthogonal range search

It is known that a kd-tree can be constructed for $n$ points ($k$-dimensional) in $O(n \log n)$ time and searching of any axis-aligned hyperrectangle can be done in time $O(n^{1-1/k} + out)$ time ...
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### Speed networking algorithm

I have 40 people and 10 tables that can accommodate 4 people at a time. The task is to make sure that every person seats with every other person at the same table exactly once, that is every person ...
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1 vote
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### Is data structure necessarily a functor?

The justification of my conjecture is that (seemly) any data structure can have a mapper that applies a given function $f$ to each element of the structure. A data structure in the end is a container ...
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### Priority queue implementation with both find-min and delete-min $o(\log n)$

Question: There are several priority queue implementations listed on Wikipedia, along with amortized complexities of each of their basic operations: Does anyone know of an implementation in which the ...
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### Formal differences between emulation and simulation?

Recently this question came up, and I've been unable to find a concrete answer. When I was reading this paper on CRDTs, I was a little perplexed by the notion of emulation here in theorems 3.1 and 3.2....
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### Are there data structures that cannot be serialized / deserialized using a context free grammar?

I understand that deserializing data from a string or binary stream into a data structure is effectively the same parsing. When you deserialize the input string, you use a grammar to create a parse ...
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### What Data Structure storing points in space for fast lookup of stored points "near" a query point?

In NLP a common problem is that you have vector embeddings of large vocabularies, and you do manipulations on these vector embeddings to compute some result vector, and then you want to find which ...
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### Alternative to binary search trees: A sorted array with empty spaces

There are many data structures that have O(log(n)) insert, delete and find operations: Self balancing binary search trees, skip lists and others. My question is: Why doesn't the following simple thing ...
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### How to show that the median cannot be maintained in $O(1)$ time?

Suppose that we have a stream of numbers $x_1,x_2,\ldots$ such that we wish to track the median of the values observed so far. This task is easy to do with $O(\log n)$ update time (where $n$ is the ...
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### Approximate (in hamming distance) subset representation

Let us have a set $S$ and a subset $T \subseteq S$. I want to find an approximate representation of $T$, i.e. I want to represent (exactly) a set $T'$ that is close to $T$. That is, I want the ...
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### Does a graph resulting from the union of triangles has a particular name?

I have different simple triangle graphs. As an instance, $G_1=(V_1,E_1)=(\{1,2,3\},\{\{1,2\},\{2,3\},\{3,1\}\})$ and $G_2=(V_2,E_2)=(\{1,4,5\},\{\{1,4\},\{4,5\},\{5,1\}\})$. The union of both graphs ...
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### How to build the tree with the "most different" solutions of a clustering?

Illustrate the question with an example : we have a similarity matrix for 1000 people, and the similarity represents how much their hobbies are the same (it does not really matter how it's built). Let'...
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### Sublinear Time Regular Expression Search

Does there exist a data structure with the following properties. Given a string $s$, it performs some polynomial amount of precomputation to construct the data structure. After construction, it allows ...
1 vote
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### Practical worst-case polylogarithmic dynamic orthogonal range queries?

There are a number of data structures in the literature that solve the dynamic orthogonal range search problem in polylogarithmic time (say, range trees). My understanding is that these structures ...
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### Unique fixed-length substrings

Input: A single long string (<10MB) and a number k Definition: A unique k-substring is a substring of length k, which occurs exactly once in the input document. Output (Approach 1): Either print ...
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### Is there a simple, intuitive explanation for why trees in Fibonacci heaps have the sizes they do?

Fibonacci heaps have a simple rule that ensures its tree sizes grow exponentially with their ranks: A node can lose at most one child. Once that child is lost, the node must be cut from its parent. ...
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### Optimal point placement on integer lattice

What is known about the following point placement problem? For positive integers $N$, $n<N^2$, and $N\times N$ grid $\mathcal{G}$, compute \begin{eqnarray*} \mu_1(N,n)\triangleq\min_{\mathcal{P}\...
644 views

### Time Complexity for Nearest Neighbor Searches in kd-trees

Nearest neighbor searches in kd-trees run in logarithmic time, as shown by Friedman et al. However, I have some difficulty to fully understand the proof. In order to calculate the average number of ...
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### Data structures for embedded simplicial complexes

I am looking for a data structure to encode an $n$-dimensional simplicial complex with an embedding in $\mathbb{R}^{n+1}$. I am aware of combinatorial maps, which generalize rotation systems of planar ...
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### Lower bounds for list/set data structures without delete

I'm interested in lower bounds on the amortized time cost for either of the following dynamic data structure problems, in the cell probe or RAM model, or any model that lets us do operations on words ...
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