# 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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### Is there a name for trees were siblinghood cannot happen between a leaf and a non-leaf?

The title of this question pretty much says it all. I would like to know if there is some standard name for trees in which, if any two nodes are siblings, then either they are both leaves, or they are ...
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### Calculation of sum of weights of nodes in a tree graph

Updated There's a real production project related to real estate properties around the world. The data has a structure of nested nodes. E.g. end nodes which have no outgoing edges (red) are properties ...
110 views

### Graphs-like data structure with weighted vertices

I am searching for literature related to a graph-like data structure where vertices are weighted instead of edges. Formally, we can define a weighted-(edge)-graph $G=(V,E, w(\cdot))$ as a tuple of ...
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### Is there a history-independent rope data structure?

I'm experimenting with a toy (functional) programming language. One of my ideas is to aggressively hash cons everything, thus representing any data structure as a single integer. In that context, data ...
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### Data Strcuture to represent dependencies amongst modules

Consider several software modules $m_1, m_2, ... m_n$. Each module has some inputs and outputs and the inputs to some of the modules are dependent on the outputs of some other modes. For example, in ...
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### Immutable Space Model

I have heard it said that time is more precious than space because we can reuse space but not time. What if we treat space with this much reverence? What is generally known about models of ...
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### 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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### Lower bound for reversing a list using queues

How do you prove (or disprove) that a list of length $n$ cannot be reversed in time $o(n \log n)$ using $O(1)$ queues? Each queue is FIFO. Time refers to the number of operations on the queues. ...
481 views

### Data structure to determine if sets are disjoint in o(n) time

My initial question was exactly the title of this post, but after feedback from commenters I have formulated a more precise version of the question that attempts to capture its essence. Does there ...
109 views

### Topology/Space of Recursive Algebraic Datatypes

I have a recursive algebraic datatype. I (somewhat arbitrarily) defined one function to compute distance between instances, and am trying to define a function to approximate a "vector" between ...
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### How fast can we find and disconnect roots in a forest?

Consider a forest of rooted trees. The problem is to support two operations: disconnect(v): if v is the root of some tree in the forest, remove all edges of v; findroot(v): find root of the tree ...
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### Improving Bloom filter - can we distinguish elements of a database using less than 2.33275 bits/element?

While we usually use large e.g. 64 bit hashes, there are many techniques to reduce this size, e.g. for savings in storage and transmission. Popular Bloom filter instead of marking just 1 hash ...
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### Suggested approach to cover data structure literature

I am not sure if this question is odd topic or too broad, but I have been wondering about this for a long time, and I would very much appreciate any valuable inputs. As a new grad student working on ...
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### Bloom filter variant for constant-time subset/superset queries

Bloom filters make it easy to determine if an element is in a set, within some acceptable margin of error. I'm looking to solve a related problem for which Bloom filters are inadequate, but for which ...
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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 ...
541 views

### Data Structure to calculate which interval a point lies in? [closed]

I have a list of $n$ non-overlapping intervals, namely $[a_1,a_2],[a_2,a_3],...,[a_n,n_{n+1}], a_i \in \mathbb{N}$. Each of these intervals has a corresponding value $v_i$ corresponding to it. Now ...
184 views

### What is known about computing distinct count range queries?

Let $U=\{1,\ldots, u\}$ be a universe of elements for some $u\in \mathbb N$. Given some $n\in\mathbb N$, we are interested in computing some function $f:U^{\le n}\to\mathbb R$ over range queries. In ...
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### Sublinear finite-precision sampling in a stream

I am looking to sample a single item from a stream such that each item in the stream has an equal probability of being selected. This is a restricted version of the reservoir sampling problem. On a ...
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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 ...
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### Reachability in Dynamic Line Graph

Given a directed line graph $G = v_1 \rightarrow v_2 \rightarrow \cdots \rightarrow v_n$, there are two operators, namely $\mathsf{move}(v_i, v_j)$: this operator moves $v_i$ to the position ...
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 ...
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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 ...
336 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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Define a partial order $\le$ on $\{0,1\}^d$ by pointwise comparison, i.e., we say $x \le y$ if $x_i \le y_i$ for all $i=1,2,\dots,d$. I am interested in the following problem: Given $x_1,\dots,x_n \... 1answer 164 views ### Algorithms in preprocessed universe [closed] In celebrated paper Clustered integer 3SUM via additive combinatorics by TM Chan and M Lewenstein one of the provided algorithms is the one for preprocessed universe. They were able to provide an ... 0answers 132 views ### Online triangle counting Please consider the following problem. It can (but probably shouldn't) be called offline version of online triangle detection on subgraphs. Given a graph$G$and a collection$C$of subsets of ... 4answers 638 views ### Purely(ish) functional data structure with fast append and forward iteration I find I have need for a data structure with a specific set of requirements: It represents an immutable sequence of values (fixed sized integers if this matters) Appending a new value to the end (and ... 1answer 1k views ### Reachability on DAG (best-known algorithm) Task: To answer several reachability queries on large DAGs (millions or billions of vertices and edges) using a data structure that takes up as little space as possible, is not expensive to construct, ... 0answers 146 views ### Range min-gap query The min-gap of an array$A[1..n]$of$n \ge 2$elements is defined as$\min_{1 \le i < j \le n}{|A_i - A_j|}$. Now, I am considering a query version of it. Given$A$, a query receives two integers$...
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 $A$ ...