poset

Finding maximal elements of a poset's subset

由 半腔热情 提交于 2020-02-03 08:52:31
问题 The problem is the following: Given a poset's subset S find the maximal elements of S. For example consider the hass diagram of the poset in http://ndp.jct.ac.il/tutorials/Discrete/node34.html. Given a subset of it ex: {12, 2, 8} the maximal elements are 12 and 8. I do not know if I describe precisly the problem. I think the problem might involves some sorting or computation of transitive closure but I am a little confused. Could you give me some approach for a fast algorithm? I would like to

Efficient algorithm to find the maximal elements of a partially ordered set

由 不羁岁月 提交于 2020-01-14 07:12:11
问题 I have a partially ordered set, say A = [x1, x2, ...] , meaning that for each xi and xj in the set, (exactly) one of four possibilities is true: xi < xj , xi == xj , xi > xj , or xi and xj are incomparable. I want to find the maximal elements (i.e., those elements xi for which there are no elements xj with xi < xj ). What is an efficient algorithm to do this (minimize the number of comparisons)? I tried building a DAG and doing a topological sort, but just building the graph requires O(n^2)

Java Poset simulation

由 橙三吉。 提交于 2020-01-07 02:01:55
问题 I'm looking to simulate a poset, called x say, of size 2n in java of the form a_1 < a_2 < ... < a_n, and b_1 < b_2 < ... < b_n. I want to run an iteration to get a random linear extension whereby I compare the 'size' of each object and if two adjacent positions can be switched I do so, if not then I stick, to end with a new order. For example x[i] = a_k and x[i+1] = b_k I switch them, however if x[i] = a_k and x[i+1] = a_(k+1) I would not. (In essence this is the Karzanov Khachiyan chain). I

Number of ways to go through a partially ordered set

由 时光毁灭记忆、已成空白 提交于 2019-12-23 18:00:44
问题 This is built upon a previous question Solve a simple packing combination with dependencies, although there is no need to check out that question to understand this one. This question asks about the fastest ways to count the number of linear extensions of a partially ordered set. Such an partially ordered list can be visualized as the feasibility of a packing configuration, given arbitrary ordering of the objects. The question is than equivalent to what are the possible ordering of all the

Java partially ordered Collection<E>

由 ≡放荡痞女 提交于 2019-12-09 02:39:51
问题 I am looking for a Java implementation of a data structure which holds a collection of elements for which a partial ordering is defined, and which allows one to iterate over those elements in some topological order (any of the possible orderings is fine; preferably a stable ordering as the contents of the collection changes). Ideally it would implement a Collection<E> , Set<E> , or SortedSet<E> interface and support all of the methods on the interface. In terms of specifying the total

Sorting a poset?

由 浪子不回头ぞ 提交于 2019-12-04 17:55:58
问题 There are a huge number of sorting algorithms out there, but most of them only work on totally-ordered sets because they assume that any two elements are comparable. However, are there any good algorithms out there for sorting posets, where some elements are uncomparable? That is, given a set S of elements drawn from a poset, what is the best way to output an ordering x 1 , x 2 , ..., x n such that if x i ≤ x j , i ≤ j? 回答1: There's a paper titled Sorting and Selection in Posets available on

Sorting a poset?

由 别说谁变了你拦得住时间么 提交于 2019-12-03 11:37:15
There are a huge number of sorting algorithms out there, but most of them only work on totally-ordered sets because they assume that any two elements are comparable. However, are there any good algorithms out there for sorting posets, where some elements are uncomparable? That is, given a set S of elements drawn from a poset, what is the best way to output an ordering x 1 , x 2 , ..., x n such that if x i ≤ x j , i ≤ j? There's a paper titled Sorting and Selection in Posets available on arxiv.org which discusses sorting methods of order O((w^2)nlog(n/w)), where w is the "width" of the poset. I
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