# 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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### What is the current state of the art with respect to First Order Bayesian Networks?

The below is a survey paper: https://ieeexplore.ieee.org/document/5579472 Is there any significant updates to this? They mention Bayesian Logic Programs (BLP), Bayesian Logic (BLOG) and Multi-Entity ...
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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 ...
180 views

### 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 $S = \emptyset$. ...
122 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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### 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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### 2D-Interval partition problem

The classical interval partition Problem ascs for a minimal colouring of an interval graph: Let [a_i, b_i] be a collection of (closed) intervals (for i in {1,2,...,n} ). Find a partition of {1,2,...,n}...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
98 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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### 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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### 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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### 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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### 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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### Finding k shortest Paths with Eppstein's Algorithm

I'm trying to figure out how the Path Graph $P(G)$ according to Eppstein's Algorithm in this paper works and how I can reconstruct the $k$ shortest paths from $s$ to $t$ with the corresponding heap ...
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### 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 ...
110 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 ...
3k views

### Number of reachable vertices in DAG for every vertex

Let $G(V,E)$ be an acyclic directed graph, such that out-degree of any vertex is $O(\log{|V|})$. For every vertex of $G$ we can count the number of reachable vertices, just by running dfs from every ...
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### 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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### 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 ...
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### Directed NP-hard problems on DAGs

Tree width measures how close a graph is to a tree. Several NP-hard problems are tractable on graphs with bounded tree width. If a problem remains NP-hard on trees then tree width cannot save us. This ...
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### Deciding transitivity of a directed acyclic graph [duplicate]

Is there any algorithm that decides whether a given directed acyclic graph is transitive or not, in time-complexity asymptotically better than boolean matrix multiplication?