# Questions tagged [sets]

Questions about finite and infinite sets and multisets, related data structures and concepts.

51 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
1k views

### Alternative to Bloom filter for extreme parameters

A Bloom filter is a space-efficient probabilistic data structure to perform membership-tests on a set (see Wikipedia's page for a definition; I use the same notations below). I am interested in a ...
158 views

### Overlap Maximization problem

Here's the problem: I have a collection of collections, $C$, where each $c\in C$ is a collection of sets $X\subset U$. Denote $c_i$ as the i-th $X$ in $c$. Informally, I want to map all the sets in ...
305 views

81 views

### Set of maximum overlaps

Assume I have a list of $N$ surfaces $\{S_i\}, i \in [1,N]$ which may or may not overlap. I also have a boolean function $F(S_{i_1},\dots,S_{i_k})$ (with $1 \le k \le N$) which tests whether all ...
42 views

### Abstract Data Type

I have been studying data structures. In that I have come across topics like Array being defined as Power set of cross product of set of objects and set of natural number and list being defined as ...
331 views

### hash-table subsets

Having trouble figuring this out. If I have 2 sets of integers how would I use a hash table to test if set A is a subset of set B (in pseudocode). I think I understand that basically I would need to ...
105 views

### Minimum overlap partitioning

We are given $N$ sets of $M$ non-unique elements each. The amount of overlap (computed as the element count in the set intersection) between the elements of these sets is stored in a $N \times N$ ...
49 views

### Smallest set non-disjoint with other given sets

Given a number of sets, what is the best algorithm to calculate the smallest set S such that S is not disjoint with any of the given sets?
70 views

30 views

### Set data structure for data too large to fit into memory

I'm trying to solve the following exercise: Given N data items and memory that can hold M/B blocks of size B. Describe a data structure that needs at most N/B blocks of external memory and allows ...
33 views

### Optimally find one of the total orderings for a poset based on some metadata about the elements

Given a finite, partially ordered set with the following two properties: Every element in the set has one of two types: "A" or "B". The type does not define the total ordering of the set and is ...
24 views

### Algorithm for finding the set of systems of distinct representatives

Given a collection of finite sets, is there an algorithm for finding the set (unordered) of all systems of distinct representatives for the collection? Example: S: {{1, 2}, {1, 2, 3}} Unordered ...
49 views

### The maximum number of uniquely intersected elements from the all possible intersection scenarios among the sets in a two-column matrix

Let us define a $n \times 2$ matrix M consisting of integer sets, such that the first column consists of the so-called intersecting sets, and the second column ...
62 views

### Find a partition of multiset of binomial coefficients with constriants

Given the multiset $S$ where the elements are defined by the binomial coefficient ${n \choose k}$ where $n \in \mathbb{N}$ and $0\leq k \leq n$ find the partition $P$ of $S$ such that the sum of ...
61 views

### Algorithm for Minimum Subset Needed to Satisfy all Constraints

I was wondering what is the most efficient algorithm to solve something like the following: You have $P$ people. You have $T$ tasks, each of which is a set of sets that represent all of the possible ...
188 views

50 views

### Data structure for overlapping sets

Is there a good data structure for storing overlapping sets? Consider having multiple sets which can overlap in various ways and would like to store them in the memory and access efficient way. ...
55 views

### How to maximize $f$ while minimizing $g$ at the same time?

Lately, I have been dealing with a problem that I didn't know how to name it to solve it properly. The problem is as follow: let's assume that we have a set of elements $A$. And, we have two ...
54 views

### Disjoint Set Connected Components With Weighted Graph

I have been trying to solve this HackerRank problem (link). The basic premise of this problem is that there is a tree with undirected, but weighted, edges. The cost of a path in this tree is taken ...
26 views

### For a collection $S$ of weighted sets $S_i$, find those $k$ elements that maximise the sum of weights of all sets $S_i$ covered by them

I have a collection $S$ of sets $S_i$. Each $S_i$ has a weight given by how many times this set was observed in some data. I now want to find the $k$ elements that maximize the cumulative weight of ...
95 views

### Pruning a powerset based on a graph

I have a list of nodes l = [1, 2, 3, ... , n] and a list of tuples p = [(1, 2), (2, 3), ...], where the latter represents which ...
116 views

### Algorithm: How many symbols of occurence k fit into b buckets under condition

I have the following problem to solve: Given a set of buckets $B=\{b_0,\dots b_n\}$ of known size, a constant $k$ < |B| and a set of symbols $S=\{s_0,\dots, s_?\}$ with unknown size. Place a total ...
What does the symbol $::$ mean in the following statement? $\forall{x}\in K :: x \longrightarrow x$ A cycle in a graph is a path that starts and ends on the same node. Clearly, if nodes in K lie on ...
Let's consider finite grid of points with size of $N$ by $M$ and set of $x$ points ($x$ is small number, up to 10, $N$ and $M$ are big numbers, up to 30000 )). Each of the $x$ points is described with ...