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# 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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163 views

### On aB-trees and its practical implementation

I'm reading the paper Succincter by M. Patrascu (link). It introduces on page 7 the aB-tree. This is a regular B-ary tree that represents an array of values. It stores the element of the array in the ...
247 views

### Dynamic and/or practical succinct data structures for triangulations

Does anybody know of any results on succinct data structures for triangulations that can be constructed efficiently, and preferably also updated efficiently? Does anybody know of practical ...
6k views

### unique binary tree from preorder and postorder traversals of a full binary tree [closed]

If we have a preorder and postorder traversals of a full binary tree T(i.e every internal node have exactly 2 children). can we uniquely construct the corresponding full binary tree T. If so.. could ...
154 views

### Combining multiple time-based datasources with different periods

I have two time-based data sources (one providing data by month and the other by week) that must be combined to create a third daily source (recognizing that at best we're getting one possible ...
488 views

### How to partition 3d Voronoi graph into n-number of balanced cuts while minimizing the number of edges that go between the parts?

I have a 3d Delaunay triangulation and I construct a Voronoi diagram from it. I have a computation algorithm: for each node of the Voronoi diagram compute a value based on values that neighbouring ...
361 views

### Formal Representation of Haskell Data-Types

I come from Haskell programming and currently writing my (Diploma/Master) thesis. I'm having trouble finding a formal/mathematical notation for a Haskell data-type. The Haskell data type is: ...
167 views

### Minimal rare subgraphs

I am looking for any related work to the following problem. Say you have a large directed graph $G$ and you want to find rare (or unique) subgraphs of minimal size that are not isomorphic to any other ...
686 views

### Name this list-of-lists data structure

Is there a canonical name for the following data structure for list of lists? Suppose we have got a list of length $Z$ of finite lists $[a_0,\dots,a_n], [b_0,\dots,b_m], [c_0,\dots,c_o], \dots$ of ...
532 views

### Continuity vs Uniformity when designing Hash functions

Reading available literature (yep, including wikipedia), I see that hash functions should have (continuity) and map values that differ very little to similar/same hash codes, in particular for (hash ...
523 views

### Lock-free, constant update-time concurrent tree data-structures?

I've been reading a bit of the literature lately, and have found some rather interesting data-structures. I have researched various different methods of getting update times down to $\mathcal{O}(1)$ ...
866 views

### Simple k-nearest-neighbor algorithm for euclidean data with highly variable density?

An elaboration on this question, but with more constraints. The idea is the same, to find a simple, fast algorithm for k-nearest-neighbors in 2 euclidean dimensions. The bucketing grid seems to work ...
5k views

### Merging Two Binary Search Trees

I'm looking for an algorithm to merge two binary search trees of arbitrary size and range. The obvious way I would go about implementing this would be to find entire subtrees whose range can fit into ...
75 views

### Load-balancing; Alternate methods of keeping track of nodes?

Reading various articles in the literature have given me only a few decent methods of keeping track of nodes before->after load-balancing them on a very large network. One popular method uses virtual-...
290 views

### Is there a name for a hashtable with a tree for each bin instead of a list?

It is well-known that the worst case performance for a chaining hashtable, is O(n), where n is the number of objects in the table. The normal assumption is that the hash is either uniform, or secure, ...
206 views

### Optimal preprocessing for certain types of queries

Suppose we have a semigroup $(S,\circ)$ with elements $S=\lbrace s_1,s_2,\dots,s_n\rbrace$. Our goal is to compute products $s_i\circ s_{i+1}\circ \cdots\circ s_j$. In their paper "Optimal ...
30k views

### Why would one ever use an Octree over a KD-tree?

I have some experience in scientific computing, and have extensively used kd-trees for BSP (binary space partitioning) applications. I have recently become rather more familiar with octrees, a similar ...
2k views

### Higher-order algorithms

Most of the well-known algorithms are first-order, in the sense that their input and output are "plain" data. Some are second-order in a trivial way, for example sorting, hashtables or the map and ...
1k views

### How do I choose a functional dictionary data structure?

I've read a bit about the following data structures: Bagwell's Ideal Hash Tries Larson's Dynamic hash tables Red-Black trees Patricia trees ...and I'm sure there are a lot of others out there. I've ...
6k views

### What are the outstanding questions in purely functional data structures?

This question is inspired by another question about what's new in PFDS since the publication of Okasaki's book in 1998. I'll start with two questions I have: Is there a purely functional set data ...
215 views

### Relational model for data structure reasoning

I am trying to find out if there is any work on applying the Codd's relational model (underlying relational databases) for reasoning about linked data structures. Any connections with UML models and ...
952 views

### Dynamic Upper Envelope of lines in the plane

There are easy algorithms to calculate the upper envelope of an arrangement of lines in the plane. See e.g. section 2.3 in the survey Davenport-Schinzel sequences and their geometric applications. ...
1k views

### Notable examples of the square root idea in complexity analysis

There are a number of algorithms and data structures which exploit the idea that $\max \left\{k, n/k\right\}$ gets its minimum value at $k=\sqrt n$. Common examples include baby-step giant-step ...
2k views

### Data Structure isomorphisms

Disclaimer: I am not a CS theorist. Coming from abstract algebra, I'm used to dealing with things that are equal up to a isomorphism - but I'm having a trouble translating this concept to data ...
1k views

### Trees that structure partially ordered data

Suppose we have a binary search tree $T$ built over keys from a totally ordered set, and we want to support the standard dictionary lookup $\mbox{Find}(x)$ which returns a pointer to the node ...
1k views

### Given a B-Tree, determine the order keys were inserted

Given a B-tree, determine what order the keys were inserted in. There may be multiple answers: I'd like to generate them all. Is there any known method for this? Or similar problems? Clarification:...
73 views

### How to automatically generate indexes and preaggregations from queries

This question might be a little ill-specified, but the idea I want to explore is: User writes a bunch of queries that they want to perform over some data (for concreteness, just consider it a read-...
387 views

### A subset lookup algorithm

Suppose I have a list $\cal X$ of subsets of $\{1, ..., n\}$. I can do preprocessing on this list if necessary. After this preprocessing, I am presented with another set $A \subseteq \{1, ..., n \}$. ...
211 views

### Optimal term frequency analysis

I'm looking for a term-frequency analysis structure which is more efficient than a hash table in terms of worst-case performance and speed in practice. I specifically care about the operations insert ...
219 views

### an efficient algorithm for mismatch profile

We have M=10000 binary sequences of length N=1000. given length L=15, for each pair of sequences, $S_1$ and $S_2$, we define the mismatch profile, mp($S_1$,$S_2$,$L$)[$m$], for m=0,1,...,L as ...
319 views

### Updates on a cache-oblivious B-tree

Lately I have been studying cache-oblivious data structures and algorithms. I was reading about the cache-oblivious B-tree from the Handbook of Data Structures and Applications, with hopes of actually ...
2k views

### Find Shortest Pairwise Distance of Points in o(n log n)?

The following exercise has been handed out to students I supervise: Given $n$ points in the plane, devise an algorithm that finds a pair of points which distance is minimal among all pairs of ...
192 views

### Tradeoff Bounds for Halfspace Range Counting

What is the current best bound for performing halfspace range counting queries on a set of $d$-dimensional points, expressed in the form of a time/space tradeoff. According to Matousek's seminal 1993 ...
533 views

### Remove specific edge from ST (link-cut) tree

ST (or link cut) trees are a special kind of trees used for dynamic graph algorithms. They support the following operations in logarithmic time: CUT(v) Deletes the edge from v to its parent JOIN(v, w)...
531 views

### Fortunes Algorithm - Beach Line Data Structure [closed]

This is a cross-post from stackoverflow. I did not recieve a good answer, I guess it is because the question is more theoretical. I have to implement Fortunes algorithm for constructing Voronoi ...
286 views

### Rearranging strings to minimise storage in a trie

I'm currently thinking about the following problem. Problem Input: a set $W$ of strings over an alphabet $\Sigma$. Goal: permute the characters in each string so that the trie that will contain the ...
720 views

### maintaining a balanced spanning tree of a growing undirected graph

I am looking for ways to maintain a relatively balanced spanning tree of a graph, as I add new nodes/edges to the graph. I have an undirected graph that starts as a single node, the "root". At each ...
2k views

### Data structure for shortest paths

Let $G$ be an unweighted undirected graph with $n$ vertices and $m$ edges. Is it possible to preprocess $G$ and produce a data structure of size $m \cdot \mathrm{polylog}(n)$ so that it can answer ...
274 views

### Self-organizing Sequential Search Heuristics

I've read the paper by Jon L. Bentley "Amortized analyses of self-organizing sequential search heuristics". It deals with different schemes for improving linear search. (such as after every access to ...
336 views

### Non-trivial applications of Bloom filters

Does anyone have some nice examples of modifying algorithms that employ a set data structure to instead employ a Bloom filter? In other words, the damage done by the Bloom filter's false positive ...
101 views

### 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 ...
918 views

### Splittable stack

What is known about data structures that can maintain a sequence of items subject to the following two operations? Push(x): add x to the end of the sequence, and return an identifier for its position ...
1k views

### parallelizable fast matrix in-place transposition

what is the current state of the art in fast and parallel matrix in-place transposition? I would be very happy, if I could be given some pseudocode for this problem. As far as I could find papers, ...
161 views

### Dynamic planar exact k-nearest neighbors for pathological data

What are the best known results for a data structure offering the following operations on sets of points in 2-dimensional euclidean space: $insert(x)$ $delete(x)$ $nearest(k,x)$ (where $k$ is an ...
547 views

### Dynamic Tree Marked Ancestor Queries

Assuming a rooted tree $T$ with vertices $V$, I am maintaining subsets of $V$, for example $M \subseteq V$ whose vertices are associated with particular labels or values. $V$ is dynamic in that it ...
420 views

### Reducing space usage of st-connectivity with multiple passes?

Suppose a graph $G$ with $n$ vertices is presented as a stream of $m$ edges, but multiple passes are allowed over the stream. Monika Rauch Henzinger, Prabhakar Raghavan, and Sridar Rajagopalan ...
591 views

### What data structures exist for fast calculation of distances between multi-dimensional points

I'm writing a program that receives data over a network connection. Every data point is simply a 4 dimensional vertex, lets call the dimensions X,Y,Z,W. The values of each dimension are exponentially ...
2k views

### Purely Functional Equivalent of B-Tree?

I am exploring the idea of writing a DBMS in purely functional way. The traditional data structure used for indexing is B-Tree. I'd like to know some purely functional equivalent of B-Tree that would ...
154 views

### Working with all leaves on a certain level of a b-tree

I want to work with a b-tree of any size. I want to do something with all leaves of the lowest depth $d$. Then if a certain condition holds, I want to recursively consider the same condition for the ...
What are some ways of commutatively combining a pair of lists to produce a list comprised of elements from the pair of inputs, with no duplicates, with time complexity better than $O(n \log(n))$? ...