Questions tagged [dag]
For questions about the usage and manipulation of Directed Acyclic Graphs (DAG).
57
questions with no upvoted or accepted answers
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Minimum Number of Edges Added to a DAG to get Unique Topological Order
The question is simple:
Given an unweighted directed acyclic graph, $G = (V, E)$, what is the minimum number of directed edges we need to add to $E$ such that the resulting graph $G = (V, E')$ has ...
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136
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Has this graph-theoretic problem got a known name? Is it NP-hard?
I am considering the following problem.
We are given a Directed Acyclic Graph. In general, there would be some number of subgraphs that, contracted into one node, would make it a tree. For example, ...
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4
votes
0
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96
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Can the running time be reduced to something lower than $O(d^4)$?
Imagine I have a weighted complete directed graph $G$ with $d$ vertices(so $d(d-1)$ edges) and I want to do the following:
Set $D$ to be a DAG with the same set of vertices but without any edges
sort ...
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4
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Fastest algorithm for shortest path with atmost k edges on a DAG with non-negative edge weights?
(Please note, this is not a duplicate to Shortest path with exactly $k$ edges OR Shortest path with a fixed number of edges. What I want is a better algorithm)
The problem under consideration is to ...
3
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33
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Online cycle detection but not quite: the Featherstitch problem
Featherstitch (Frost et al., 2007) is an approach for representing data consistency requirements for disk storage. This question concerns a graph-theoretic problem (§4.1 in the paper) that its ...
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3
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103
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Using vector clocks vs. directed acyclic graph for causality detection in distributed systems
I'm trying to understand how vector clocks compare to DAGs for causality detection in a distributed system.
When trying to detect causality relations in a distributed system, a very commonly proposed ...
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3
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114
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Order the vertices to maximize the weights of edges in the induced subgraph
I have a complete directed graph $G:=(V,E)$ with directed edge weights $c_{ij}$ for every distinct nodes $i$ and $j$.
Goal: Find the topological order such that the smallest edge weight of the ...
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3
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183
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Assign weights to the edges in a DAG so that, for all S and T, all paths from S to T have equal weight
I have a DAG, and on each edge, I have a minimum and maximum weight. I would like to assign (or determine it's impossible to assign) exact weights to each edge so that
Each edge's weight is between ...
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3
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0
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506
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Transform a DAG to fork-join format
I have a directed acyclic graph where the nodes are tasks and the edges are dependency relations between tasks - the edges go from the dependency to the task that depends on it.
It is possible that ...
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3
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1k
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Lowest single common ancestor in a Directed Acyclic Graph?
I was reading how to find the Lowest common ancestor in a DAG. A DAG can have scenarios where the LCA yields multiple solutions and I feel the accepted answer explains that pretty well.
However, one ...
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3
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0
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371
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Context-free grammar for DAGs?
I'm looking for a "safe" representation of DAGs. With "safe" representation I mean that it can be described by a context-free grammar. Ideally, this grammar would be suitable for a simple LR parser.
...
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2
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84
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Finding a maximum induced DAG in a digraph
I have a digraph D on n vertices formed in the following manner:
I start with k ordered (not sorted) lists of integers, with each integer from 1-n in at least one list. Integers do not show up more ...
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2
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0
answers
257
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Finding unique topological ordering wrt to another vertex ordering
Given a directed acyclic graph with $n$ nodes labeled from $1$ to $n$, what is an efficient way to produce the unique topological ordering with lower labeled nodes prioritized over higher labeled?
...
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2
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84
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maximally exclusive paths in a DAG
Suppose we have a DAG $G$ with one source node $s$, ie. it has a path to every node, and target node $t$ which every node has a path to it. For a pair of paths from $s$ to $t$ we can define a distance ...
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593
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Find all rooted subgraphs of a DAG
I searched the exchange and couldn't seem to find an answer to this.
I am trying to find an algorithm that, given a directed acyclic graph (DAG) $G = (N,E)$ with a single root node $r\in N$, finds ...
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2
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0
answers
109
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How do I merge these lists?
I ave a a collection of lists of objects:
$a_1$ $a_2$ $a_3$...
$b_1$ $b_2$ $b_3$...
$c_1$ $c_2$ $c_3$..
I need to merge them into a minimal possible number of lists, each list must be as long as ...
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2
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0
answers
120
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Max Flow on low depth DAGs
I have a family of acyclic networks in which every path from the source of a given network to its target has length exactly $3$. I'm aware of a publication that in general, finding a max flow in a DAG ...
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0
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86
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Topological sort of DAG that minimizes maximum number of unique-source-edges crossing through any node when placed in 1-d line
Consider a DAG such as one shown below:
How do I find a particular topological order of nodes, such that when the nodes are placed in a straight line, the maximum number of unique-edges that cross ...
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1
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0
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92
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Reverse one edge to make the most expansive strongly connected component
Problem statement
We're given a directed simple acyclic graph with weighted vertices. Find an edge $e$ such that reversing it would create a strongly connected component (SCC) whose price is maximal. ...
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124
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Directed Acyclic Graph with minimized merging nodes
Suppose that we have a set of paths that all of them strat from the source "I" and end to the destination "O". The paths might have shared nodes. We are allowed to change the ...
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1
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0
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17
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Aggregating pairwise ratings in a graph
A finite set of individuals provide bounded non-binary pairwise ratings of other individuals (say, -10 to +10), forming a directed graph (cycles possible).
I'd like to determine aggregate ratings for ...
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1
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181
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Determining whether DAG is semi-connected
I have been asked to write an algorithm which determine whether a DAG is semi-connected. (Recall that a DAG is semi-connected if for any pair of vertices $x,y$, there is either a path from $x$ to $y$ ...
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1
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0
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83
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minimising Longest-Path in DAG
Assume we have weighted DAG (directed-acycle-graph), source s and target t.
Define the number of edges as $E$.
Given $0<\alpha<1$:
Choose $\alpha*E$ edges to cut their weight by half so that the ...
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1
vote
0
answers
32
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How to compute all inequivalent (under Aut(P)) nonnegative integer weight assignments (with fixed sum) to the vertices of a finite poset P?
Let $P$ be a poset on $n$ points, $\text{Aut}(P)$ its automorphism group, and $a_1,a_2,\dots,a_k$ the lengths of the orbits under $\text{Aut}(P)$.
Goal: An algorithm to generate a member from each ...
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1
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0
answers
66
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What does a recursive min s,t-cut optimize?
Consider the following algorithm sketch:
Given an edge-weighted directed acyclic graph $G = (V, E, w : E \to \mathbb{N})$, adjoin a temporary source $s$ and sink $t$ to get $G' = (V', E', w')$. $G'$ ...
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0
answers
20
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In a DAG, what is the name of the process replacing no branch path with a single vertex
In my work, I meet a process for DAG, and need to explain it in my report. So, I would like to know the name of the process.
The process is very simple. The vertices of degree two except roots and ...
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1
vote
0
answers
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Is there a data structure to represent changes to a DAG over time, with fast reproduction of instances of the DAG?
Consider a directed acyclic graph (DAG) of topics and links. Apart from the root topic, topics are situated under one or more parent topics, and links, as well, are situated under one or more parent ...
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1
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66
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Proof that "the last vertex in any postordering (in a DFS) of G lies in a source component of G"
From the book Algorithms (Jeff Erickson), there's a lemma that states:
The last vertex in any postordering of G lies in a source component
of G
My initial reaction to this was that the proof would ...
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1
vote
0
answers
43
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Optimally find one of the total orderings for a poset based on some metadata about the elements
Given a finite, partially ordered set with the following two properties:
Every element in the set has one of two types: "A" or "B". The type does not define the total ordering of the set and is ...
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1
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0
answers
20
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Shortest sequence of jobs, with dependencies, subject to capacity constraints
Suppose I have $n$ courses, some with some prerequisites, and I can take up to $k$ courses in a semester. I want to compute the least number of semesters needed to complete all courses, while ...
D.W.♦
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1
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0
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519
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Obtaining a graph with no cycles after removing k edges
I am looking for an algorithm that upon an input of a directed graph G and a natural number k,outputs a set of k edges, that upon removing them, the graph will have no cycles. If there are no such k ...
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1
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0
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171
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Finding all non-comparable nodes in DAG
I have a DAG and I want to list all pairs of vertices that are not comparable (there is no path from the first to the second or the second to the first).
In this image (taken from this StackOverflow ...
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1
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0
answers
149
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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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1
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0
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33
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Routing a DAG through 5 consecutive butterfly networks
I have two questions concerning the paper Nearly linear-size holographic proofs. In the second paragraph of section 6, A Graph Coloring Problem, it is claimed that
Using standard packet-routing ...
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1
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0
answers
204
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Algorithm for finding single input/output sub graphs
I'm running into an interesting directed acyclic graph (DAG) problem and was wondering if this is a known problem and if it has an efficient algorithm for it. I will use 'graph' and 'DAG' ...
1
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1
answer
174
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Generating project network graph
I had a problem of generating project network graph (like there and there) from list of activities and their dependencies.
Informal description:
Every activity is represented as edge of directed ...
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0
answers
55
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DAGs and Equivalence Class of DAGs
I am learning DAGs and Equivalence Class of DAGs, I am reading the material by Prof. Campos Ibáñez here: https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume18/acid03a-html/node2.html
However, I ...
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1
vote
0
answers
412
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Multithreaded algorithm to traverse DAG
I have a DAG of tasks designed as:
DAG {
Dictionary<NodeAddresses,Node>
}
Node {
List<Node> Parents;
List<Node> Children;
Task T;
}
...
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1
vote
0
answers
392
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Compression of a complete Directed Acylcic Graph
Consider a DAG $g$ as a label $l$ with a list of sub-nodes $\bar{g}$:
$g ::= l \enspace \bar{g}$
This is an "unfolded" representation of the DAG, i.e. it contains double entries, when two paths ...
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1
vote
0
answers
226
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Maximum weighted antichain over a DAG with cardinality constraint
Let $G=(V,E)$ be a vertex weighted DAG (Directed Acyclic Graph), with positive real valued weights.
Let also $k\leq \left\vert V\right\vert$, is there any way to find a maximum weighted antichain ...
1
vote
0
answers
93
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Problem with update in Dynamic Bayesian Networks
Consider the following Bayesian network:
I want to impose constraints that state that a node can only be true (1) if at least one of its parents are true (1). So, for node $C$, the constraint takes ...
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1
vote
0
answers
108
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Fully dynamic k-shortest-path
I have a directed acyclic graph with positive edge weights. It is constantly changing in that nodes are deleted and added. For each change, I need to find the $k$ shortest paths.
My current approach ...
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0
answers
26
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Tree Width of Directed Graph
I'm Nestor Mermoz Thea. I have two definition over the Directed strong pseudoforest and Directed weak pseudoforest that I don't really well understand.
Directed weak pseudoforest: A directed weak ...
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0
answers
96
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Using topological sort to find inconsistencies represented by cycles in directed graphs
Consider the following scenario.
Let $x_1,...,x_n$ be a group of cars that all drive from some point A to some point B. Each car starts driving in index order. i.e. $x_1$ starts driving strictly ...
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61
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DAG graph where indegree >= outdegree and indegree = 0 => outdegree <= 1, cover all vertex with min amount of paths
Given a graph $G = (V, E)$ where
G is directed: $ \forall \ e \in E$ : $e$ has a direction.
G is acyclic (no cycles): $ \forall$ path $v_1, \dots , v_n : (v_n, v_1) \not\in E $.
If indegree $\gt0$, ...
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0
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52
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Minimise vertex loss converting DCG to DAG
I have a DCG that I want to lay out with the parents on the left and children to the right. I want to maximise the number of all children present to the right of all parents whilst minimising the ...
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0
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87
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Dijkstra algorithm for DAG
Assuming we have a K-Partite DAG (edges are directed from one level to the next) with edge weights either 0, 1 or 2.
We are looking for the shortest path between a node from group 0 to group k-1 (path ...
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0
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98
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Minimum weight $k-$path cover on a DAG proof verification
Suppose you are given a directed acyclic graph $G$ with $n$ vertices and an
integer $k \leq n$. Each edge has an associated weight $w(u,v)$. We want to find $k-$vertex-disjoint paths that cover all ...
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0
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49
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identify nodes with paths of unique length from source
Let us consider a Directed Acyclic Graph $G(V,E)$ such that all edges have unit weight. Let $s$ be a source node, $s\in V$ and a set of destination nodes, $D\in V\backslash s$. My problem is to find a ...
0
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0
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49
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Given start strings, find simplest DAG that constructs target strings by concatenation
Say we have a number of start strings (green) and a number of target strings (red). Two strings can always be concatenated to a new string which can then be arbitrarily often reused (two arrows in, (1,...
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