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Questions tagged [partial-order]

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Algorithms for unordered vertices of the convex hull

For the sake of this question a "non-ordering" "set of vertices of convex hull" algorithm produces the collection of all points on the convex hull of its input without producing ...
worldsmithhelper's user avatar
1 vote
1 answer
88 views

What happens when two different nodes have the same Lamport clock ID

With Lamport clocks, each node keeps its own counter. Before sending a message, a node increments its counter by one: LC(A)=LC(A)+1, and sends ...
A. Darwin's user avatar
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1 answer
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Ranked voting method where unranked candidates on a preference list aren't taken to be the least preferred?

Say there are 5 candidates, A, B, C, D, and E. An election is held using a ranked voting method. That is to say, each voter submits a preference list (the order in which they prefer candidates). E.g. ...
chausies's user avatar
  • 532
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0 answers
49 views

Creating a partial order from a total order with a concurrency oracle

I have a total order represented as a Hasse diagram (basically a linked list of ordered elements) and a concurrency oracle. The concurrency orracle is a function, that tells me which pairs of elements ...
Minop's user avatar
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3 votes
0 answers
103 views

Map-like data structure with subsets as keys

I am looking for a map-like data structure with the following properties: it uses subsets of some set S as keys. The size of S is potentially unbounded, but does not change during the runtime the ...
Minop's user avatar
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2 votes
0 answers
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Algorithm for finding an embedding of a cover diagram

I am making some notes on order theory for my own self study (and certainly anyone else that wants to read them). I'm impressed with what mermaid can do out of the ...
Galen's user avatar
  • 125
1 vote
1 answer
30 views

Terminology for number of topological sorts

Is there a standard terminology for the topological sort count over a partial order? I went with magnitude of a poset rather than dimension as this is too close to linear algebra terminology. I wonder ...
ExpressionCoder's user avatar
1 vote
1 answer
58 views

relation based on a given partial order - does it have a name?

Let $P$ be a partial order on $X.$ Does the relation $E(P)=$ { $(x,y)\in (X\times X)\setminus P:P$ $\cup$ { $(x,y)$ } is a partial order on $X$ } have a name? If not, what's a good thing to call it?
mathematrucker's user avatar
1 vote
1 answer
93 views

Is there any Algorithm to check a vertex\node's partial order in terms of other vertices\nodes for a given graph?

For the given figure, let's consider vertex v3. For v3, v0 has a higher partial order,v1 & v2 has the same partial order, and v4 & v5 have lower order than v3, e.g., higher: {v0}, same: {v1,v2}...
skdr's user avatar
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34 views

Iterative algorithm for assembly index? [duplicate]

DOI: 10.3390/e24070884 provides pseudocode for computing the assembly index of an object. It is written as recursive algorithm, which might be fine. But I would like to implement an iterative version ...
Galen's user avatar
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3 votes
1 answer
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Lamport Timestamps and Causality

I'm having trouble understanding lamport timestamps in practice and how they guarantee causal ordering. Definitions Lamport defines the "happens before" relationship in his paper. He states ...
RSHAP's user avatar
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3 votes
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Data structure for finding greatest lower bound with respect to a partial order

I have some partial order $\preceq \,\,\subset A \times A$, I'd like a data structure with the following operations: $Insert(a, x, T)$: add $(a, x)$ to the collection $T$ $Find(x, T)$: find the ...
Jake's user avatar
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0 votes
1 answer
55 views

Define a directed edge in a DAG using partial ordering

I am trying to describe a novel type of DAG's construction algorithm. The directed edges of the graph corresponds to a partial ordering: i.e. any directed edge $e$ spanning from $f$ to $t$ also ...
Domi's user avatar
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1 vote
0 answers
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How to compute all inequivalent (under Aut(P)) nonnegative integer weight assignments (with fixed sum) to the vertices of a finite poset P?

Let $P$ be a poset on $n$ points, $\text{Aut}(P)$ its automorphism group, and $a_1,a_2,\dots,a_k$ the lengths of the orbits under $\text{Aut}(P)$. Goal: An algorithm to generate a member from each ...
mathematrucker's user avatar
1 vote
0 answers
68 views

Finding all minimal upper bounds in a partially ordered set

I have a partially ordered set of numbers, represented as a vector<set<int>> (e.g. if $2 \preceq 4$ in this order, then ...
Alexey Romanov's user avatar
1 vote
1 answer
72 views

Efficient cardinality of set overlap relation

Assume that we have a set S of sets s. Every pair (s,s') in ...
Radio Controlled's user avatar
1 vote
1 answer
38 views

How do we know that $F^{n + 1}(\overrightarrow{\emptyset}) = F(F^n(\overrightarrow{\emptyset}))$?

I am currently studying the textbook Principles of Program Analysis by Flemming Nielson, Hanne R. Nielson, and Chris Hankin. Chapter 1.3 Data Flow Analysis says the following: The least solution. The ...
The Pointer's user avatar
1 vote
1 answer
67 views

Showing that $F$ is a monotone function

I am currently studying the textbook Principles of Program Analysis by Flemming Nielson, Hanne R. Nielson, and Chris Hankin. Chapter 1.3 Data Flow Analysis says the following: The least solution. The ...
The Pointer's user avatar
0 votes
0 answers
149 views

Methods for generating DAG with small Minimum Path Cover

On a directed acyclic graph $G=(V,E)$ the Minimum Path Cover (MPC) is the minimum number of paths that can be constructed on the DAG such that all vertices are covered by at least one path. If one was ...
shgr1092's user avatar
3 votes
0 answers
44 views

Components of subset partial order

Given a collection C of sets, there are a number of proposed algorithms for building the subset partial order, e.g. this paper. But is there any work on algorithms ...
Radio Controlled's user avatar
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2 answers
105 views

Finding connected components without building the graph first

What are good algorithms for finding connected components in a graph defined by a set of elements X, where each x in ...
Radio Controlled's user avatar
1 vote
2 answers
64 views

Why is there so little literature on partial order production?

Please excuse or improve the poor title of this question. My question is rather undirected, but I guess I am trying to find out if I might be missing a keyword for my problem. So there is plenty of ...
Radio Controlled's user avatar
1 vote
0 answers
46 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 ...
luisfer's user avatar
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2 votes
0 answers
36 views

What are all linear extensions of the product order of $\{1, \dots, M\} \times \{1, \dots, N\}$?

Note: I have read somewhere that finding all linear extensions of a partial order is in general a #P-complete problem (which apparently means difficult, and thus no closed form expression), but just ...
hasManyStupidQuestions's user avatar
0 votes
2 answers
47 views

Scheduling: Existence of specific total order

A question arising from a scheduling problem: I have a finite set $X$ with elements $x_i$ and some preorder $\leq$. I have pairs $p_j$ of $x_i$ (i.e. $p_j$ = $(x_k, x_l)$) with the property that $x_k \...
Moritz's user avatar
  • 103
0 votes
2 answers
324 views

Efficiently computing minimal elements over partially ordered sets

I have a list of sets that I would like to sort into a partial order based on the subset relation. In fact, I do not require the complete ordering, only the minimal elements. If I am not mistaken, ...
Radio Controlled's user avatar
3 votes
1 answer
71 views

Computing minimum partition of poset of $N$ intervals into chains in $o(N^{2.5})$ time?

Consider a set $P$ of $N$ intervals $\{I_i = (l_i, r_i)\}$ partially ordered according the standard interval order: $I_i < I_j$ iff $r_i \le l_j$. I want to find a minimum cardinality partition of ...
dysonsfrog's user avatar
1 vote
0 answers
20 views

Construct neighbourhood relation graph for n sequences

Given $n$ sequences with length $m$, $s_i=\langle c_1^ic_2^i\dots c_m^i\rangle, i = 1,\dots, n$, where $c^i_j\in D$ is a partial ordered set and the partial order relation $\sqsubseteq$ on $D$ answers ...
cgcgbcbc's user avatar
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2 votes
0 answers
33 views

Poset data structure to find least element, greater or equal to given

Let $A$ be a finite set, and $S \subset \mathcal{P}(A)$. Is there a data structure for $S$ that would allow to quickly retrieve an element $q \in S $, given a key $p \in \mathcal{P}(A)$, such that $q$ ...
Zyx's user avatar
  • 145
3 votes
0 answers
80 views

Measuring the Union of Products of Intervals

Verbose Motivation for this Question Inspired by this paper about how the problem of counting unlabelled subtrees that are unique up to isomorphism is #P-complete, I was thinking about the problem ...
Zach Hunter's user avatar
1 vote
1 answer
109 views

Does every Partially Ordered relation and its dual have the same number of topological orderings?

Given the Hasse Diagram of a Partially Ordered Relation, is it the case that both the POSET itself and its dual POSET have the same number of topological orderings? I have tried a few examples, and ...
Lakshay Kakkar's user avatar
3 votes
0 answers
132 views

Matching relative order in subsequence of fixed length

I encountered this problem from game development which I will formulate in a more formal way: Given a sequence $A = a_1, a_2, \dots, a_m$ and a permutation of $\{1, \dots, n\}$, $B = b_1, b_2, \...
Jingjie Yang's user avatar
1 vote
1 answer
44 views

Is this algorithm for partial ordering of sets complete and sound?

I need to build a partial order tree of sets for analysis. Where the order is defined as A <= B <=> for all x in A, y in B, x <= y. I realized that if ...
epiqueras's user avatar
  • 113
5 votes
1 answer
85 views

Algorithm to establish a global ranking given individual rankings

I am looking for an algorithm(s) that can compute a global ranking (partial ordering) given individual rankings, in some kind of principled manner. I want to establish a partial-ordering of some ...
Daniel Kats's user avatar
3 votes
0 answers
140 views

effective, efficient algorithms on antichains

In a partially ordered set L, an antichain is a subset A of L such that no two elements of A are comparable. Antichains are commonly used to represent upward-closed subsets of L, that is, sets S such ...
David Monniaux's user avatar
2 votes
1 answer
82 views

Counting number of permutations respecting partial order

Suppose that we have an array $A$ of $n$ elements with some partial order known, e.g. for example as a $n\times n$ matrix containing $c_{ij} \in \{-1, 0, 1\}$ where $0$ represents unknown and $-1, 1$ ...
orlp's user avatar
  • 13.6k
5 votes
0 answers
361 views

How to convert a dependency graph to series-parallel representation?

I'm given a finite partial order, in the form of a dependency graph between items, and I'd like to have it in series-parallel form (Wikipedia). So formally, given a finite partial order $\le$ on a ...
MarnixKlooster ReinstateMonica's user avatar
1 vote
1 answer
46 views

Checking if the mimimum is unique

We have a finite poset and its subset $S$. We can enumerate elements of $S$ using an iterator. I need to check if there are more than one minimal elements of $S$ (regarding the above poset). The ...
porton's user avatar
  • 493
2 votes
0 answers
139 views

Two related partial order relations

We will consider a set whose elements I call "precedences". Precedences are related by two relations: "is subclass of" and "higher than", which are specified by some pairs (given on algorithm input) ...
porton's user avatar
  • 493
1 vote
0 answers
42 views

Minimize number of comparisons to discover a strict total order

$S$ is a set of $n$ elements with some unknown strict total order. The goal is to discover the greatest $k$ elements, where each step consists of comparing $m\ge 2$ elements at once (so if we compare $...
Fricative Melon's user avatar
1 vote
1 answer
314 views

The sorting problem for partially ordered sets

I have two questions about sorting for posets, one easy and one hard: Easy: Suppose we have a set of objects and a partial order. Given any two objects such that $a \leq b$, we want to delete $b$ ...
Mike Battaglia's user avatar
3 votes
0 answers
550 views

Transform a DAG to fork-join format

I have a directed acyclic graph where the nodes are tasks and the edges are dependency relations between tasks - the edges go from the dependency to the task that depends on it. It is possible that ...
Daniel's user avatar
  • 31
0 votes
0 answers
28 views

Retroactively ordering actors' concurrent activity on disjoint sections of a data-structure

Hi! I'm new here, a terrible computer-scientist, and have no idea what I'm doing; I'm more expecting / hoping for links to research on algorithms or data-structures that contribute to problems like ...
ELLIOTTCABLE's user avatar
3 votes
1 answer
140 views

Efficiently determine relative ordering between two elements in a PO-set

What algorithms/heuristics exist for efficiently determining the relative order between two elements in a partially ordered set? In my case, the PO-set is stored as a directed acyclic graph where an ...
Filip Haglund's user avatar
1 vote
2 answers
106 views

How to solve this partial order reduction in $O(n^2)$?

There are two orderings of numbers from the same set. Number $a$ is "immediately before" $b$ iff $a$ appears before $b$ in both sequences and there is no other number that appears between them in both ...
hazrmard's user avatar
  • 121
0 votes
0 answers
249 views

Longest chain of pair of points

For chaining two points A and B ...
user avatar
8 votes
1 answer
883 views

Finding longest chain in poset in subquadratic time

Let $(A,\leq)$ be some finite poset. For $a,a' \in A$ we can determine in constant time whether or not $a \leq a'$. The height of an $A$ is by definition the greatest $n$ such that there are elements $...
Mees de Vries's user avatar
5 votes
2 answers
86 views

How to efficiently determine whether a relation is total?

I have a set $S$ of pairs $(x_1,x_2)$ with $x_1,x_2 \in X$ for some set $X$. I want to know whether this defines a total relation on $X$. In other words, whether: If $(a,b)$ in $S$ and $(b,c)$ in $...
wythagoras's user avatar
4 votes
1 answer
172 views

Disproving well-quasi-order by providing an infinite anti-chain

I am currently studying the theory behind Well-Quasi-Orders. However I am having some issues in understanding how an infinite anti-chain can be produced to disprove the claim that a partial order $P$...
jjohn's user avatar
  • 474
3 votes
1 answer
289 views

Generalized sorting algorithm on partially ordered set generated by a relation

Assume we have a finite set $X$ of elements and any relation $\preceq$ on $X$. Such a relation may or may not generate a reflexive transitive anti-symmetric relation $\leq$ on $X$ (a partial order). ...
Werner Thumann's user avatar