Questions tagged [transitivity]
13 questions
21
votes
7 answers
in O(n) time: Find greatest element in set where comparison is not transitive
Title states the question.
We have as inputs a list of elements, that we can compare (determine which is greatest). No element can be equal.
Key points:
Comparison is not transitive (think rock paper scissors): this can be true: A > B, B > C, C > A…
James Wierzba
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17
votes
8 answers
Is transitivity required for a sorting algorithm
Is it possible to use a sorting algorithm with a non-transitive comparison, and if yes, why is transitivity listed as a requirement for sorting comparators?
Background:
A sorting algorithm generally sorts the elements of a
list according to a…
HugoRune
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3
votes
0 answers
Does this endomorphism over finite automata have a name?
I found this function that can be applied onto a DFA to produce a DFA. Is there a name for it?
Above: A simple DFA over the alphabet $\{0, 1\}$
Below: The resultant DFA over the alphabet $\{0\mathrm{$}, 1\mathrm{$}, 00, 01, 10, 11\}$
You can think…
Brett Schreiber
- 124
- 5
3
votes
1 answer
Changing a relation to become transitive
Given a binary relation $R$ on a finite set $S$, is there an efficient algorithm to transform $R$ to a transitive relation $R'$ by minimum number of addition or deletion of pairs $(x,y)$ to or from $R$ where $x,y \in S$?
Dandelion
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- 13
2
votes
1 answer
Algorithm for getting symetric vertex sets of undirected graph
For my application problem, I am searching for an algorithm that can find all symmetric vertex sets of an undirected labeled graph.
My definition of symmetric vertex set is:
Let $G$ be a graph with vertex set $V$ and edge set $E = \{u,v\}, u,v \in…
Pepper M
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2
votes
1 answer
Simplest way to check edge set for transitivity
I'm playing around with tournaments and currently have the problem that I need to check whether a given subset of the edges of a tournament is transitive (it need not be acyclic). I'm aware that I can always take the transitive closure of the edge…
G. Bach
- 2,019
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2
votes
1 answer
Is this a valid encoding of a tree structure using set theory and a valid way to extract the leaves from it?
I'm looking to formally define a tree and then extract the leaves from it in a concise way.
Does this look ok?
What is the best way of doing this?
$
Y = \{a,b,c,d,e,f,g\} \\
R = \{a \mapsto b, a \mapsto d, d \mapsto e, d \mapsto f, f \mapsto g\} \…
newlogic
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2
votes
1 answer
Like transitive reduction, but removing vertices rather than edges?
Suppose I have a directed graph $G = (V, E)$ (or, which is the same, a relation on the set $V$ as defined by the adjacency matrix) that may contain three vertices $x, y, z$, such that $xy, xz, yz \in E$ — that is to say, the relation restricted to…
Ignat Insarov
- 249
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1
vote
1 answer
Check if a relation is reflexive, symmetric and transitive
I want to better understand how this actually works, as my solutions are
sometimes not 100% correct.
I have the following relation:
Check if the following relation is reflexive, symmetric, and/or
transitive:
$$ R_1 = \{ (x,y) \mid x,y \in…
Prometheus
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1
vote
0 answers
Transitive reductions of transitive closure
Is there a name for the relationship between two DAGs A,B where B is one of the transitive reductions of the transitive closure C of A?
For example the connectivity of nodes in both graphs would still be the same.
For example, we can connect all…
Radio Controlled
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1
vote
0 answers
coloring of an interval graph with constraints
Given an interval graph that represents a set of tasks, in a given period of time, to be assigned to a set of employees, the objective is to find a minimum coloring of this graph such that the total duration of the tasks corresponding to each color…
Farah Mind
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0
votes
1 answer
Reflexive transitive closure = (zero or more) Kleene star?
In Alloy Tutorial they denote some reflexive transitive closure with Kleene star saying that they admit zero or more elements at that position.
// File system is connected
fact {
FSObject in Root.*contents
}
In Alloy, in can be read as…
Little Alien
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0
votes
2 answers
Can someone point out why these directed graphs aren't equivalence relations?
As far as I can tell, these two directed graphs are reflexive, symmetric and transitive.
Luke D
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