Questions tagged [dag]

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

54 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
5
votes
0answers
286 views

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 ...
5
votes
0answers
135 views

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, ...
4
votes
0answers
92 views

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 ...
4
votes
0answers
4k views

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
votes
0answers
25 views

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 ...
3
votes
1answer
92 views

How to generate, validate, and invalidate a set/list of numbers in O(1) time and space?

Imagine my server is generating "tokens" of some sort for a client on a regular basis. When a client asks for a token, the server responds with a new value (and any other supplemental ...
3
votes
0answers
100 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 ...
3
votes
0answers
162 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 ...
3
votes
0answers
1k views

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 ...
3
votes
0answers
308 views

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. ...
2
votes
2answers
148 views

Ordering of operations in a DAG of git commits

Context: I'm looking for a better state resolution algorithm for https://github.com/MichaelMure/git-bug Summary of the current algorithm and shortcomings git-bug is a distributed bug-tracker that ...
2
votes
0answers
63 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 ...
2
votes
0answers
249 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? ...
2
votes
0answers
390 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 ...
2
votes
0answers
68 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 ...
2
votes
0answers
449 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 ...
2
votes
0answers
105 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 ...
2
votes
0answers
117 views

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 ...
1
vote
0answers
21 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 $y$ ...
1
vote
1answer
49 views

Maximum flow in integer flow network

Let's say you have a maximum integer flow function in a network with 7 directed edges, meaning the flow cannot be increased anymore. The capacity of each edge is then increased by one. The capacity of ...
1
vote
1answer
59 views

House Robber DP Algorithm (Not three in a row)

This is a similar question to A variant of the house robber problem but instead of the general case, I'm wondering how you would solve the standard house robber problem, but when you cannot rob from ...
1
vote
0answers
47 views

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 ...
1
vote
0answers
30 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 ...
1
vote
0answers
59 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 $G' = (V', E', w')$. $G'$ ...
1
vote
0answers
18 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 ...
1
vote
0answers
60 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 ...
1
vote
0answers
28 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 ...
1
vote
0answers
36 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 ...
1
vote
0answers
16 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 ...
1
vote
0answers
298 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 ...
1
vote
0answers
118 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 ...
1
vote
0answers
32 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 ...
1
vote
0answers
149 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' ...
1
vote
1answer
147 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 ...
1
vote
0answers
50 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 ...
1
vote
0answers
368 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; } ...
1
vote
0answers
362 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 ...
1
vote
0answers
194 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 ...
1
vote
0answers
87 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 ...
1
vote
0answers
105 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 ...
0
votes
0answers
21 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 ...
0
votes
0answers
31 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 ...
0
votes
0answers
13 views

--Graphical Models-- Understanding blocked paths and conditional independence

I am quite confused by this slide from a course I found on the internet from UCL on Graphical Models. Here is the slide: I would like to confirm whether I have correct understanding: In the following ...
0
votes
0answers
43 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 ...
0
votes
0answers
47 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 ...
0
votes
0answers
33 views

Iterative Deepening DFS for DAGs

Does Iterative Deepening DFS only guarantee the shortest path for DAGs, assuming a visited list is used to prevent infinite cycles? I can't seem to find any answers online specifically related to ...
0
votes
0answers
22 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,...
0
votes
0answers
48 views

Transitive reductions of transitive closure

Is there a name for the relationship between two DAGs A,B where B is one of the transitive reductions of the transitive closure <...
0
votes
0answers
115 views

Methods for generating DAG with small Minimum Path Cover

On a directed acyclic graph $G=(V,E)$ the Minimum Path Cover (MPC) is the minimum number of paths that can be constructed on the DAG such that all vertices are covered by at least one path. If one was ...
0
votes
1answer
37 views

Generating topological sequence from DAG with additional "not appearing before" constraints

DAG specifies the relationship of one node must appear after another. What if I add an additional constraint where one node cannot appear before another on top of the DAG? Is there an algorithm for ...