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For questions about the usage and manipulation of Directed Acyclic Graphs (DAG).

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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 ...
ryan's user avatar
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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, ...
gigabytes's user avatar
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4 votes
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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 ...
Johannes's user avatar
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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 ...
Loves Probability's user avatar
3 votes
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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 ...
Alex Shpilkin's user avatar
3 votes
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103 views

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 ...
Gerard Yin's user avatar
3 votes
0 answers
114 views

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 ...
Johannes's user avatar
3 votes
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183 views

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 ...
Paul Accisano's user avatar
3 votes
0 answers
506 views

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 ...
Daniel's user avatar
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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 ...
aug's user avatar
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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. ...
vog's user avatar
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2 votes
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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 ...
Dave's user avatar
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2 votes
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257 views

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? ...
eLibrarian's user avatar
2 votes
0 answers
84 views

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 ...
Ameer Jewdaki's user avatar
2 votes
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593 views

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 ...
Erik M's user avatar
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109 views

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 ...
Ruby's user avatar
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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 ...
G. Bach's user avatar
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1 vote
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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 ...
nepee's user avatar
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1 vote
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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. ...
tomashauser's user avatar
1 vote
0 answers
124 views

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 ...
Payam's user avatar
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1 vote
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17 views

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 ...
vsekhar's user avatar
  • 111
1 vote
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181 views

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 $y$ ...
NWiz95's user avatar
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1 vote
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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 ...
Amran Tomer's user avatar
1 vote
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32 views

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 ...
mathematrucker's user avatar
1 vote
0 answers
66 views

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 $G' = (V', E', w')$. $G'$ ...
taktoa's user avatar
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1 vote
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20 views

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 ...
Light Yagmi's user avatar
1 vote
0 answers
90 views

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 ...
Eric Walker's user avatar
1 vote
0 answers
66 views

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 ...
user126667's user avatar
1 vote
0 answers
43 views

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 ...
luisfer's user avatar
  • 11
1 vote
0 answers
20 views

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.'s user avatar
  • 154k
1 vote
0 answers
519 views

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 ...
pseudoturing's user avatar
1 vote
0 answers
171 views

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 ...
Petr Hudeček's user avatar
1 vote
0 answers
149 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 ...
Zakir's user avatar
  • 111
1 vote
0 answers
33 views

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 ...
Olivier Bégassat's user avatar
1 vote
0 answers
204 views

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' ...
Mattias De Charleroy's user avatar
1 vote
1 answer
174 views

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 ...
Elman's user avatar
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1 vote
0 answers
55 views

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 ...
user2842390's user avatar
1 vote
0 answers
412 views

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; } ...
edeboursetty's user avatar
1 vote
0 answers
392 views

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 ...
choeger's user avatar
  • 610
1 vote
0 answers
226 views

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 ...
ALVARO ALEXIS FLORES's user avatar
1 vote
0 answers
93 views

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 ...
jonem's user avatar
  • 371
1 vote
0 answers
108 views

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 ...
eirirlar's user avatar
  • 111
0 votes
0 answers
26 views

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 ...
Nestor Mermoz Thea's user avatar
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0 answers
96 views

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 ...
user1da901's user avatar
0 votes
0 answers
61 views

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 $\gt0$, ...
borekking's user avatar
0 votes
0 answers
52 views

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 ...
AJP's user avatar
  • 101
0 votes
0 answers
87 views

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 ...
Philip L's user avatar
0 votes
0 answers
98 views

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 ...
AspiringMat's user avatar
0 votes
0 answers
49 views

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 ...
user49739's user avatar
0 votes
0 answers
49 views

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,...
2080's user avatar
  • 191