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Journal ArticleDOI

A phase transition phenomenon in a random directed acyclic graph

Boris Pittel, +1 more
- 01 Mar 2001 - 
- Vol. 18, Iss: 2, pp 165-184
About: 
This article is published in Random Structures and Algorithms.The article was published on 2001-03-01. It has received 22 citations till now. The article focuses on the topics: Vertex (graph theory) & Directed acyclic graph.

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Citations
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Book ChapterDOI

Causal sets: Discrete gravity

Rafael D. Sorkin
TL;DR: These are some notes in lieu of the lectures I was scheduled to give, but had to cancel at the last moment as mentioned in this paper, and they at least give a feel for the subject and convey some of the excitement felt at the moment.
Journal ArticleDOI

A dynamic topological sort algorithm for directed acyclic graphs

David J. Pearce, +1 more
- 09 Feb 2007 - 
TL;DR: A new algorithm is presented that, although it has inferior time complexity compared with the best previously known result, its simplicity leads to better performance in practice and an empirical comparison against the three main alternatives over a large number of random DAGs is provided.
Journal ArticleDOI

Random graph models for directed acyclic networks

Brian Karrer, +1 more
- 15 Oct 2009 - 
TL;DR: This work proposes two specific models roughly analogous to the fixed edge number and fixed edge probability variants of traditional undirected random graphs for directed acyclic graphs, finding that theory and measurements agree surprisingly well-far better than the often poor agreement of other random graph models with their corresponding real-world networks.
Journal ArticleDOI

Evidence for a continuum limit in causal set dynamics

David Rideout, +1 more
- 13 Apr 2001 - 
TL;DR: In this paper, the authors find evidence for a continuum limit of a particular causal set dynamics which depends on only a single coupling constant p and is easy to simulate on a computer.
Journal ArticleDOI

Poset limits and exchangeable random posets

Svante Janson
- 01 Nov 2011 - 
TL;DR: A theory of limits of finite posets in close analogy to the recent theory of graph limits is developed, and representations of the limits by functions of two variables on a probability space, and connections to exchangeable random infinite posets are studied.
References
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Journal ArticleDOI

The transitive closure of a random digraph

Richard M. Karp
- 01 Mar 1990 - 
TL;DR: It is shown that, when n is large and np is equal to a constant c greater than 1, it is very likely that all but one of the strong components are very small, and that the unique large strong component contains about Θ2n vertices, where Θ is the unique root in [0, 1] of the equation.
Journal ArticleDOI

An improved algorithm for transitive closure on acyclic digraphs

Klaus Simon
- 01 Jun 1988 - 
TL;DR: An improvement on the algorithm for finding the transitive closure of an acyclic digraph G with worst case runtime O(n·ered) and space O( n·k, where k is the width of a chain decomposition.
Journal ArticleDOI

On the Maximal Number of Strongly Independent Vertices in a Random Acyclic Directed Graph

Amnon B. Barak, +1 more
- 01 Dec 1984 - 
TL;DR: In this article, the authors define a subset of vertices in a random acyclic directed graph to be strongly independent if there is no directed path between any pair of nodes in the subset.
Journal ArticleDOI

On the Probability of Connectedness of a Random Graph $\mathcal{G}_m (t)$

V. E. Stepanov
- 01 Jan 1970 - 
Journal ArticleDOI

Random graph orders

Michael H. Albert, +1 more
- 01 Mar 1989 - 
TL;DR: In this paper, the transitive closure of a random graph order was studied and it was shown that the expected height and set up number of Pn are sharply concentrated around cn and °n respectively.