# 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 ...
458 views

### Reusing 5-independent hash functions for linear probing

In hash tables that resolve collisions by linear probing, in order to ensure $O(1)$ expected performance, it is both necessary and sufficient that the hash function be from a 5-independent family. (...
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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 ...
107 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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### Algorithms from the Book.

Paul Erdos talked about the "Book" where God keeps the most elegant proof of each mathematical theorem. This even inspired a book (which I believe is now in its 4th edition): Proofs from the Book. If ...
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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. ...
476 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 ...
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### One Stack, Two Queues

background Several years ago, when I was an undergraduate, we were given a homework on amortized analysis. I was unable to solve one of the problems. I had asked it in comp.theory, but no ...
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### 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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### Powerful Algorithms too complex to implement

What are some algorithms of legitimate utility that are simply too complex to implement? Let me be clear: I'm not looking for algorithms like the current asymptotic optimal matrix multiplication ...
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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 ...
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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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### 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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### Succinct data structures survey?

Fischer's paper this month reminded me how little I know about the art of succinct data structures, and algorithms to use them. For those that don't know about succinct data structures: Given a ...
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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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### What is a zipper, and how does it relate to a tree-like structure?

I was reading a chapter in LYAH which didn't really make sense to me. I understand that zippers can arbitrarily traverse a tree-like structure, but I need some clarification on it. Also, can zippers ...
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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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### Comparison-based data structure for finding items

Is there a data structure that takes an unordered array of $n$ items, performs preprocessing in $O(n)$ and answers queries: is there some element $x$ on the list, each query in worst time $O(\log n)$? ...
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### 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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### Most efficient algorithm to compute set difference?

What is the most efficient algorithm to compute the difference between two set data structures? In particular, the algorithm should efficiently discover elements in the first set that are also in the ...
### How many ephemeral stacks are required to simulate a queue in worst-case $O(1)$ time?
In "Real Time Queue Operations in Pure LISP" (ML implementation), Hood and Melville show an $O(1)$ worst-case simulation of a queue using 6 stacks and global rebuilding. Can a real-time queue be ...
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 ...