Questions tagged [directed-acyclic-graph]

This is a mathematical structure composed of a set of points or vertices and a set of connectors or edges. The edges connect the vertices and those vertices are directed. Also no cycles or in other words a directed edge that connects a vertex to a vertex are disallowed.

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Positive topological ordering

Suppose I have a directed acyclic graph with real-number weights on its vertices. I want to find a topological ordering of the DAG in which, for every prefix of the topological ordering, the sum of ...
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Given a weighted dag, is there an O(V+E) algorithm to replace each weight with the sum of its ancestor weights?

The problem, of course, is double counting. It's easy enough to do for certain classes of DAGs = a tree, or even a serial-parallel tree. The only algorithm I have found which works on general DAGs in ...
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Combinatorics of Bellman-Ford or how to make cyclic graphs acyclic?

Roughly speaking, my question is: How costly is to make a cyclic graph acyclic while preserving all simple $s$-$t$ paths? Let $K_n$ be a complete undirected graph on vertices $\{0,1,\ldots,n+1\}$. (...
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Why is “topological sorting” topological?

Why is "topological sorting" called "topological"? Is it just because it determines an order without altering any vertices or edges -- like a doughnut and coffee cup are topologically equivalent? Why ...
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Computing topological sort while keeping edges “short”

Motivation: I want to compute a topological sort order in which the connected vertices are close to each other. Problem statement: Given a DAG $G(V,E)$ with $n$ vertices, compute a topological sort ...
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Canonical labeling of special classes of DAGs

Graph Isomorphism of directed acyclic graphs (DAGs) is known to be GI-complete. So a polynomial time algorithm to canonize DAGs is not known. What are some special classes of DAGs that can be ...
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Restricted Reachability Problem

Let $G$ be a directed acyclic graph with $V$ vertices and $E$ edges. Choose some subset of $n\leq V$ "special" vertices $\{v_i\}_{i=1}^n$. How efficiently can we preprocess $(G, \{v_i\})$ so that we ...
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Minimum cost topological ordering

We are given a $n$ vertex directed graph $G=(V,E)$ and also given a cost function $c:V\times [n]\to \mathbb{R}$. Consider a topological ordering of the vertices, $v_1,\ldots,v_n$, the cost of the ...
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Generation of unlabeled acyclic digraphs

I'm looking for an algorithm to efficiently generate all unlabeled acyclic digraphs of a given order. (By "unlabeled" I mean that no two of the generated digraphs should be isomorphic.) Thanks Edit: ...
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Is the isomorphism problem between posets represented by DAGs GI-complete?

Given two directed acyclic graphs, how hard is the problem of checking whether the partial orders they represent are isomorphic? Is this problem GI-complete? I believe this problem is equivalent to ...
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