# 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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### What is known about data structures for encoding a set while considering approximate Rank queries?

Consider a universe $\mathcal U\triangleq \{1,2,\ldots n\}$, and assume that we are given a set $S\subseteq \mathcal U$. There are many data structures that allow storing $S$ while answering Rank ...
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### Random sampling data structure with removal

I'd like a data structure with the following operations: create a new instances from an array of floating point weights. randomly sample, returning an item with probability proportionate to its ...
0answers
357 views

### Set Intersection lower bounds

Consider $S_1, ...,S_n \subseteq [U]$ where size of $U$ is polylogarithmic in $n$. We allow infinite time to pre-process these sets and then ask queries of the form $S_i \cap S_j$ is empty or not. We ...
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1answer
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### Fast Algorithm to Check if a Set of Sets forms an Anti-chain

Given a set $S$ of sets, what is the fastest algorithm to check if elements of $S$ form an anti-chain with respect to subset ordering? That is, how can I quickly decide if there exists two sets $A$ ...
1answer
331 views

### For a given binary-search tree obtain an isomorphic splay tree

I will assume that the reader is familiar with some undergraduate algorithms and data structures. To people who are not familiar with splay trees I recommend to read through this link : https://en....
1answer
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### What are the must-read search trees paper?

I would like to ask a help from researchers who conduct a research in an area of search trees. Could you please write the list of the must-read papers and most recent papers which are important to ...
2answers
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### Quick-select contiguous subarray

Motivated by the question from this blog post, the following data structure question seems interesting and fun to me. Preprocess: A list of numbers $A = a_1,...,a_n$ Query(s,t,k): Return the $k$-th ...
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171 views

### What is the curve of “search vs. insert”

Consider a collection of numbers (of arbitrary size), and an oracle that is able to accept two such numbers $a,b$ and answer queries of the form $a<b, a>b, a=b$ in constant time. With this ...
0answers
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### Framing the Count-Min Sketch as a Random Projection?

The count-min sketch data structure is used to estimate the frequencies of individual elements in a data stream. The authors note that the analysis of their data structure is simpler than other ...
1answer
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### Why use two separate tables in cuckoo hashing?

I've been reading a number of papers on cuckoo hashing, including several that generalize it by talking about cuckoo hashing with multiple tables, cuckoo hashing with a stash, the (multi)graph-...
2answers
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### Constant-time bounds on offline 2-choice hashing?

I'm reading up on cuckoo hashing and came across Michael Mitzenmacher's blog posts on the subject. In his motivation of why cuckoo hashing seems like a reasonable strategy, he mentions a connection to ...
1answer
211 views

### Two papers give contradictory bounds on linear probing. How do I resolve the disparity?

I've been reading over two papers recently. The first, "Why Simple Hash Functions Work: Exploiting the Entropy in a Data Stream" proves that, assuming there is sufficient entropy in a data source, ...
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### Hashtable vs cache-oblivious [closed]

I'd like to know more about real performances of data structures, in particular two families attract my interests: hash tables cache oblivious My researches didn't find any "comprehensive" (let me ...
1answer
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### Generalized Priority Queues

I was wondering if there is any literature on the following problem: Maintain a set $S$ where each element is a function from $\mathbb{R}$ to $\mathbb{R}$ supporting the following operations: Insert ...
3answers
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### How to design concurrent data structures?

I previously asked this question on Programmers.SE, without success. I'm looking for written learning resources on how to design concurrent data structures. I'm more interested in the design process (...
1answer
487 views

### Huffman Tree Depth, Is there any theory?

I'd like to as a variation on this question regarding Huffman tree building. Is there any theory or rule of thumb to calculate the depth of a Huffman tree from the input (or frequency), without ...
2answers
216 views

### Ordered-file maintenance

I am studying the Advanced Data Structures material and I'd like to implement the Ordered-file maintenance data structure. I have few questions in order to start. The papers rely on a static view, ...
1answer
340 views

### Algebra and algebraic data types

Which of the well-known structures of modern algebra (monoids, groups, rings etc) can be expressed as algebraic data types (ADTs)? Presumably a free monoid can be considered to be isomorphic to the ...
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1answer
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### Improved lower bounds or upper bounds on union-find structures since Tarjan?

In 1979, Robert Tarjan published "A Class of Algorithms Which Require Nonlinear Time To Maintain Disjoint Sets", which proved an upper bound of $O(m \alpha(n))$ time on the time complexity of ...
1answer
162 views

### Lossless Compression Books

I am intrigued by compression techniques and I'd like some recommendations about books to study, specifically, on lossless compression algorithms and data structures. I don't know if there is a ...
2answers
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### Min Hamming distance of a given string from substrings of another string

Let $U$ be a small finite set. Consider the following problem: Input: two strings $u \in U^k$ and $v\in U^n$ with $k \leq n$. Output: a (contiguous) substring of $v$ of length $k$ with the minimum ...
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### Equilvalence among two Scheduling problems

I have two problems for scheduling: Packets arrive at a router. Router schedules them i.e. router determines which one will go out first and which one last. Here, the problem is which packet to send ...
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### Self-Aggregating Tree

Say I have a finite $n$-ary tree where each node contains state. For the sake of argument, let's say a key-value store. If we are interested in the aggregation of some key(s) at some node, then we ...
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### Triangular range counting query in poly-logarithmic time

What is the minimal space requirement for triangular range counting queries in plane if one wants to process each query in poly-logarithmic time? In [Goswami et al, 2004] they preprocess the ...
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### Purely Functional Representations of Catenable Sorted Lists question

Good day. I'm currently reading the paper "Purely Functional Representations of Catenable Sorted Lists" by Tarjan and Kaplan[link to the paper]. But I have a question about the modified 2-3 finger ...
1answer
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### Split find-min data structure that finds several small elements?

The split find-min data structure is initialized with a sequence of elements $e_1,\ldots,e_n$, each associated with a key. The data structure supports three operations: (1) $Split(e_i)$ that splits ...
1answer
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### Defintion of a Data Structure? [closed]

Lately I have been looking around for a formal definition of a what a data structure is. I cannot find neither a paper, nor a book with such a definition. Even the famous "The Art of Computer ...
1answer
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### Set query in a universe with overlapping sets

Suppose we have a universe $U$ of $n$ items $u_1,u_2,u_3,...,u_n$. And a collection of sets (no restriction on being disjoint or exhaustive etc.) which cover some items. Size of each set is bounded by ...
1answer
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### How can I formalize key value stores with set theory? [closed]

I'm currently developing a simple key-value NoSQL store and want to build its formal model. I'm interested in knowing if there some work about formalization of key-value stores outside of category ...
1answer
845 views

### Array implementation of dictionary data structure

Is there a data structure that supports searching, inserting, deletion in worst-case O(log n) time and that satisfies the following "array implementation" property: at any point in time, the data ...
2answers
633 views

### Fun with inverse Ackermann

The inverse Ackermann function occurs often when analyzing algorithms. A great presentation of it is here: http://www.gabrielnivasch.org/fun/inverse-ackermann. $$\alpha_1(n) = [n/2]$$ \alpha_2(n) = ...
2answers
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### Data structure for dynamic memory allocation

Think of the cell-probe model. Is there a data structure that can allocate contiguous chunks of memory of any length (like e.g. malloc in C), and free them, while avoiding memory segmentation, and ...
1answer
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### Looking for easy applications of fractional cascading

I want to give a couple of talks on fractional cascading, one of which will focus on applications. I'm looking for applications that make use of the full version of fractional cascading, not just the ...
1answer
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### Sorted intervals query

I'm in search for a data structure which efficiently operates over closed intervals with the following properties: dynamically add or remove an interval set, and anytime change, a number ("depth") ...
1answer
237 views

### Persistent data structures in RAM computational model

Always when I read about any efficient persistent data structures they use pointer computational model. I'm wondering if you know any efficient implementation which uses power of RAM model?
1answer
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### Array-like data structure with O(1) worst-case concatenate/join?

I am looking for a data structure $D$ which supports the following operations (preferably a (binary) tree-like structure): $D$ is indexed, i.e. there is a mapping from $\{1, \ldots, n\}$ to items ...
0answers
208 views

### Rebalancing balanced binary search tree when decreasing all keys to the right of a path?

Given a balanced binary search tree, suppose I have an operation decrease-right-keys(k, s) that operates as follows: when I call this operation on a tree $T$, I decrease all keys by $s$ in the right ...
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### Is there a purely functional vector with O(1) access to the front and back but O(log n) concatenation?

Context: For fun and perhaps for actual use, I'm making my own programming language that would compile to Typed Racket, a statically-typed Lisp dialect. One of the major features I want to implement ...