# 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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### 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 ...
28 views

### Splay trees as dynamic weight-balanced trees?

Given a collection of keys $x_1 < x_2 < \dots < x_n$ with associated weights $w_1, w_2, \dots, w_n$, a weight-balanced tree for the keys $x_i$ with weights $w_i$ is defined as follows: The ...
75 views

### Points of a finite set wihtin a ball

I am looking for data-structures to store efficiently a set of points $E$ in an euclidean space of dimension $d$. In particular, I would like to be able to solve the problem of finding all the point ...
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### \alpha-path on Euclidean graphs

Consider the following problem: Suppose we are given a G=(V, E) Euclidean Graph in the plane and a real $\alpha > 0$. For simplicity assume, there exists only one path whose summation of weights ...
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### Information theoretic lower-bound on object graph serialization

This might be a daft quesstion, but here comes. I became intriqued about data serialization formats and tried to look for research on what could be the information theoric lower bound on encoding ...
61 views

### 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 ...
66 views

### Best Asymptotic Complexity for Persistent Union Find

In this paper https://www.lri.fr/~filliatr/ftp/publis/puf-wml07.pdf, they claim to have a practically fast persistent union-find data structure for most use-cases, but it's still not polylogarithmic ...
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### What is the name of this data structure? (hash table with a limit on the number of entries)

Denote $[n] \triangleq \{1,2,\ldots,n\}$. Assume we would like to have a data structure $S$ which kinda works as a dictionary from $[k]$ to $[v]$, and supports add/remove/update/query functionality, ...
54 views

### What should I read to learn about the different models of computation used in algorithm and especially data structure analysis?

Are there any good surveys? Courses? Lecture notes? I'm especially interested in material with practice exercises, if any is available. Thanks!
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### What are some examples where the Catalan numbers show up in algorithms/data structures?

For some variants of RMQ data structures, the number of Cartesian trees (i.e. the Catalan numbers) is a part of the running-time analysis. What are some other examples where the Cataln numbers show up ...
105 views

### Binary Search Tree DELETE survey

In helping out @bapi-chatterjee on a BST question , when it came to teasing out the combinatorics of BST_DELETE(i) I ran into a wall where even under the conservative assumption that the parent tree ...
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### What effect would using different types of orders have on a binary search tree?

Recently, I was coding a comparator function for use in a set backed by a binary search tree, and the set kept saying that it didn't contain elements that I had previously added to it. I eventually ...
42 views

### Updating set of lists dependent upon a few indices

I'm curious about a data structure for a set of "valid lists", where you have a set of lists of length $i$ $S_i$, have a list $L$ of possible items to append, and a boolean function $f$, and wish to ...
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### Efficient update of the keys in associative container

I need to maintain a set $\langle(k_1, v_1), (k_2, v_2), \dots, (k_N, v_N)\rangle$ of key-value pairs subject to the following update operation. Given two keys $a < b$ and a "shift" value $C$ as ...
555 views

### Is the running time of Boyer-Moore linear?

With pattern length $M$, text length $N$, and alphabet $\Sigma$, is the asymptotic running-time of Boyer-Moore $O(N/|\Sigma|)$ (even when $M$ grows larger than $|\Sigma|$)? Are there any sublinear ...
I have a problem that I think should have been studied. I am looking for algorithms for it. Each item is a set of key-value pairs. Let $x$ be an item and $F$ be a set of items. Each key and each ...