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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1answer
52 views

random sampling DAGs via nilpotent matrix sampling

The adjacency matrix of an acyclic graph is known to be a nilpotent matrix (all eigenvalues are zero). I am interested in sampling DAG adjacency matrices or equivalently sample random nilpotent ...
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Nontrivial Time Complexity for Implicit Deep Copy

Can an imperative programming language which supports deep copying be implemented in a way where deep copies take polylogarithmic time and all other operations have polylogarithmic overhead compared ...
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1answer
104 views

Survey on Erdős-Pósa?

Does anyone know of any good surveys on Erdős-Pósa? I am particularly interested in what are the latest results for the bounding function for directed and even cycles in planar and minor free graphs ...
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37 views

Directed tree decompositions on subtrees of DAGs

Given a DAG, is the arboreal decomposition of the DAG with the guarantee that given a node $x$, $v$ such that $x$ is reachable from $v$ are in the subtree of $x$? If not, is there a similar ...
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1answer
137 views

Obtaining Sets of Ancestors Quickly in a Directed Acyclic Graphs

Suppose I have a DAG, $G = (V, E)$ and we know that all nodes in the DAG have at most $A$ ancestors. Let $V' \subseteq V$ be a subset of vertices of $V$. Is there a way to obtain the set of all ...
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Finding nodes with enough unique ancestors

Given a DAG $G = (V, E)$, let $T \subseteq V$ be a set of nodes of $V$ that is computed via the following process. Assuming the nodes of $G$ are sorted in topological order, $v_1, \dots, v_n$. We ...
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1answer
60 views

Separating DAGs using separators consisting of lists of nodes and all ancestors

Suppose we are given a DAG, $G = (V, E)$ where $n = |V|$. We consider the sets $J_1, J_2, \dots, J_n$ to be lists of vertices where list $J_i$ consists of vertex $v_i \in V$ and all ancestors of $v_i$....
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reordering a DAG with the minimum changes

Consider a DAG $(V,A)$ with an initial permutation $(v_1,v_2,…,v_n)$. We want to arrange the $n$ vertice in topological order while keeping as many vertices as possible. The problem is: Is it NP-hard ...
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74 views

Minimum feedback arc set for dense directed graph

This is really a matrix problem, but the theory I believe lies in graphs. Consider some matrix $A$ and permutation matrix $P$, where we define $\tilde{A}:= PAP^T$. I want to pick $P$ such that if $\...
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1answer
141 views

Isomorphism of ‘ordered’ DAGs / acyclic semiautomata

I am wondering what is known about the isomorphism problem on ordered DAGs, in particular how to find a canonical representative modulo isomorphism. By ordered I mean that each vertex has a list of ...
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Find all paths between specially paired nodes in a DAG in linear time

If I have a DAG with 2n nodes partitioned into n pairs of nodes with e edges, is there a ...
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1answer
99 views

Complexity of acyclicity of a “nondeterministic” graph

By "nondeterministic" I mean the graph is a collection of sets of "candidate" edges sharing a single destination: $E \subseteq 2^V \times V$. The problem is whether it is possible ...
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Best known bounds on feedback arcset in high-girth directed graphs?

I asked this question over at MathOverflow, but thinking about it a little more I think it is a more natural fit here. Let $G$ be a directed graph with $n$ vertices and $m$ edges such that every ...
5
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1answer
130 views

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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Lighting up all elements of a poset by toggling upsets

I consider the following game on a finite poset $(P, <)$. At each point of the game, I have a set of elements $S$ of the poset which are "on", and all others are "off". Initially $S = \emptyset$. ...
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1answer
207 views

Breaking cycles in network graph by adding nodes and rerouting edges

I have a quite "common" need : making a directed graph (with one or several cycles) a directed acyclic graph (DAG). But the way I want to achieve it is, I guess, way more specific : I would like to ...
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52 views

Directed Acyclic Graph partition into minimum subgraphs with a constraint

I have this problem, not sure there is a name for it, wherein a Directed Acyclic Graph has different colored nodes. The idea is to partition it into minimum number of subgraphs with the following 2 ...
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Common techniques for the acyclic orientation problem under some special constraint?

An acyclic orientation of an undirected graph is an assignment of a direction to each edge(an orientation) that does not form any directed cycle and therefore generates a directed acyclic graph(DAG). ...
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1answer
2k views

Number of simple paths between two vertices in a DAG

Let $G = (N, A)$ be a connected acyclic digraph (DAG). Furthermore, let $s \in N$ and $t \in N$ be two vertices on this graph, such that $t$ is reachable from $s$. My problem is: how many simple $s-t$...
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141 views

Crime prevention using graph theory and machine learning

I am looking for a way to the model the incidence of crime among a network of individuals. Part of it will use machine learning, and part of it will have to resort to some graph theoretic ...
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1answer
132 views

Finding Cheapest n-Path [closed]

Given a weighted directed acyclic graph, how can I find the cheapest path from an Origin Vertex to a Destination Vertex which ...
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154 views

Directed NP Hard Problem on DAG

There are problems that are NP-Hard on undirected graphs(maximum weight independent set and graph coloring) but are polynomial time solvable on trees. Tree decomposition is a good tool to talk about ...
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1answer
354 views

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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116 views

min weight k-closure on DAG

The problem Given a (connected) DAG $G(V,E)$ where each node is assigned an (non-negative) integer weight an integer k where $0\leq k\leq|V|$ Find a induced subgraph $H$ of $G$ consisting of $k$ ...
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1answer
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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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1answer
145 views

What is the name of this algorithm on direct acyclic graph?

I am trying to linearize the history of a git branch for display purpose. I want commits to be collocated by branch instead of simply displaying commits in the order given by the time of commit. In ...
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120 views

Generalized path cover problem in DAG

Let $G=(V,E)$ be a directed acyclic graph. Two vertices is transitive if there is a directed path between them. A Path Cover for a Set of Transitive Pairs (PCSTP) is a set of directed paths such that ...
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1answer
315 views

Efficient algorithm for generating data dependency DAG from lists of memory ranges and access modes

Assume you are given: A list of N (not necessarily distinct) memory ranges of the form [x,y], where x and y are non-negative integers representing the lower and upper bounds of the range, and A list ...
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1answer
668 views

How to design an algorithm which turns an undirected graph into directed with all nodes of indegree higher than 0? [closed]

Given an undirected graph $G=(V,E)$ devise an algorithm that will check whether its edges can be directed in such a way that the vertices of the resulting directed graph will all have indegree higher ...
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1answer
111 views

Multiple source shortest path with one reversal [closed]

Lets say we have a directed graph G, with vertices V, that have lengths l. I need to find the shortest path between every ordered pair of vertices in the graph, with the following constraint: In a ...
11
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1answer
364 views

Generalization of Dilworth's theorem for labeled DAGs

An antichain in a DAG $(V, E)$ is a subset $A \subseteq V$ of vertices that are pairwise unreachable, namely, there are no $v \neq v' \in A$ such that $v$ is reachable from $v'$ in $E$. From Dilworth'...
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157 views

Two-player zero-sum games in extensive form represented as directed acyclic graphs

The following is a way to represent two-player zero-sum games in extensive form. Consider a directed acyclic graph $G$ where each non-terminal vertex is one of 3 types: player 1 vertex, player 2 ...
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186 views

NP-completeness of a specific topological sorting problem

Consider $(V, E)$ be a DAG, and $p_1, \dots, p_n$ be its topological sorting (i.e. such permutation $p$ of $V$ that $\forall(x, y) \in E.\ p^{-1}(x) < p^{-1}(y)$). Let's call the goodness of $p$ a ...
11
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1answer
789 views

Enumerating topological sorts of a vertex-labeled DAG

Let $G = (V, E)$ be a directed acyclic graph, and let $\lambda$ be a labeling function mapping each vertex $v \in V$ to a label $\lambda(v)$ in some finite alphabet $L$. Writing $n := |V|$, a ...
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1answer
601 views

Ordering of a DAG minimizing some definition of cost

Consider a DAG $(V,A)$ with a topological ordering $(v_1,v_2,\ldots,v_n)$. I define the cost of this ordering as the maximum over all $1\leq i\leq n$ of $|\{j\leq i \mid \exists k>i: (v_j,v_k)\in A\...
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622 views

Tree decomposition for DAGs

Tree decompositions and treewidth are a standard way to measure how close an undirected graph is to a tree. I am studying decompositions of directed acyclic graphs (DAGs), and have come to define them ...
17
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1answer
802 views

Reference for mixed graph acyclicity testing algorithm?

A mixed graph is a graph that may have both directed and undirected edges. Its underlying undirected graph is obtained by forgetting the orientations of the directed edges, and in the other direction ...
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1answer
1k views

Longest path in a DAG that's not too long

The problem I am interested in is a simple variant of the longest path problem on DAGs: find a path between two chosen vertices in a DAG such that the sum of the weights of its constituent edges is ...
5
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928 views

Is there a linear-time algorithm for max flow on dags

What is the fastest known algorithm for max flow on dags? Can there be a linear-time algorithm running in time $O(|V|+|E|)$? Input: a weighted dag $G=(V,E,w)$ where $E$ is given as an edge list $E$ ...
13
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2answers
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Lexicographically minimal topological sort of a labeled DAG

Consider the problem where we are given as input a directed acyclic graph $G = (V, E)$, a labeling function $\lambda$ from $V$ to some set $L$ with a total order $<_L$ (e.g., the integers), and ...
14
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1answer
428 views

How expensive may it be to destroy all long s-t paths in a DAG?

We consider DAGs (directed acyclic graphs) with one source node $s$ and one target node $t$; parallel edges joining the same pair of vertices are allowed. A $k$-cut is a set of edges whose removal ...
2
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1answer
76 views

What does the contention-free communication assumption really mean in the context of DAG scheduling?

In many papers about DAG (directed-acyclic graph) scheduling in distributed systems, the authors make the assumption that the communication between the processors of the system where the DAG is ...
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2answers
842 views

Shortest path in DAG with path dependent arc costs

I've got the following problem Consider a DAG $G=(V,E)$ with $V=[v_1,…,v_n]$, and edge-set $E=[e_1,…,e_m]$, with associated costs $c_1,…,c_m$. The problem is to find the shortest paths from an ...
9
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1answer
229 views

When does a graph admit an orientation in which there is at most one s-t walk?

Consider the following problem: Input: a simple (undirected) graph $G=(V,E)$. Question: Is there an orientation of $G$ satisfying the property that for every $s,t \in V$ there is at most one (...
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2answers
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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 ...
2
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1answer
162 views

An edge orientation procedure to generate all acyclic orientations of a graph

Consider the following scheme for enumerating acyclic digraphs (DAGs) by orienting the edges in an undirected graph $G$ with $n = ||V||$ vertices: (1) Generate all $n!$ possible permutations $p_i$ of ...
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0answers
134 views

Realization of a bipolar orientation by a mixed graph

Given an undirected graph $G(V,E)$ and a bipolar orientation $s$ over $G$, consider the problem of identifying $s$ by finding the minimum number of edges such that when orienting them in a particular ...
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127 views

Minimum Weight Ordering of nodes on a directed graph

I'm bumping my head against the wall trying to prove this problem is NP-complete (it might not be) Let $G = (V,E)$ be a directed graph with weights $w:E \to \mathbb{R_{\geq 0}}$ on the edges. The ...
5
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154 views

Indexing structure for all-pairs min-cuts in a huge DAG

I have a huge DAG - e.g., the dependency graph of all packages in a linux distribution. Suppose I'd like to make a user-friendly tool that makes it very easy to understand how to break the transitive ...
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1answer
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All pairs shortest paths in a DAG [closed]

I have studied the Floyd-Warshall and Johnson algorithms. I am trying to understand if the all pairs shortest paths research in a directed graph G can be implemented in a more efficient way if I ...