# Questions tagged [directed-graphs]

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### How to find a "short" walk that visits all vertices of a strongly connected directed graph

I am interested in the following algorithmic problem: Given a strongly connected directed graph $G$, I want a "short" (see below for what I mean by short) walk that starts with an arbitrary ...
35 views

### Is there a fully dynamic algorithm to find a minimum arborescence (like Chu–Liu/Edmonds' algorithm)?

Given a weighted directed graph with nonnegative edge weights and a vertex $r$ designated as root, at each step I will do one of the following: Add a new edge to the graph. Remove an edge from the ...
• 101
1 vote
155 views

### Minimum edges removed to turn a strongly connected graph into an acyclic graph

If I start with a directed graph that is strongly connected, is there a straightforward way / algorithm to find the smallest set of edges to remove, such that the result is a directed but acyclic ...
26 views

### Is the min-cut size of a directed graphs transpose the same as that of the original?

I was wondering whether the transpose of graph maintains the same size of the minimal cut in a directed graph (digraph). This may be trivial as I haven't been able to find anything here or on Google ...
1k views

### Linear-time algorithm for determining the presence of incomparable pairs in a directed acyclic graph (DAG)

I am seeking a linear-time algorithm to determine whether a directed acyclic graph (DAG) contains at least one pair of incomparable nodes. Two nodes $u$, $v$ are said to be incomparable if there is ...
• 43
24 views

### Balanced Directed Graph Realization

I have a list of integers: each integer represents a node in a directed graph, and the value of the integer is both the desired indegree and outdegree of said node. Some research suggests that this is ...
• 103
103 views

### How to divide weakly connected graph into "k" weakly connected subgraphs (using e.g. networkx)?

I have a weakly-connected weighted digraph $G$, and I'd like to divide it into $k$ weakly connected subgraphs $G_k$ each with approximate equal total weight $w_{T_k}$ ($w_{T_k}$ = sum of weights of ...
1 vote
49 views

### What is a good heuristic for multi-point A* on a directed graph?

I am conducting a stateful search of a large graph in an effort to find some solutions of minimal cost. With an admissible heuristic for estimated time to completion from a given state (as in A*), I ...
• 11
638 views

### Structural equivalence of self-referential structures

Given two types, T1 and T2, how does structural equivalence work when they're self-referential? Further, how do we go about proving it? ...
351 views

### Turning an undirected graph into a directed graph such that in-degree of all nodes is at most 1 or show it is not possible

I was thinking what if you just started with the node with lowest non-zero degree $u$ (only count undirected edges) and picked random edge that is connected to that and direct that inwards. EX: ...
• 121
42 views

### Which algorithm solves the single-pair shortest path in a weighted directed cyclic graph?

I need to find the shortest path between two nodes in a directed, positively weighted graph that migt contain cycles. All weights are either zero or one. If it was not weighted, I'd use breadth-first ...
• 3
1 vote
525 views

### Algorithm for finding a path in a directed graph that visits each node in a given subset

I was wondering about a solution for the following problem: Given a directed graph $G=(V,E)$ and a subset of vertices $U \subseteq V$ suggest an algorithm that finds if there is a directed path that ...
• 275
1 vote
184 views

### (Directed) Graphs: Minimal Vertices Subset With No Outgoing Edges

I've been trying to study some graph algorithms and, as part of it, prove a bunch of graph theorems in order to practice my ability to do theoretical work with graphs. Specifically, I've been trying ...
• 113
55 views

### Directed graph of bank balances and transactions, how to process transactions?

I'm working on a game where there are several different entities represented by nodes. Each node has a starting balance, and directed edges show where money is owed from one account to another. One ...
461 views

### Find a simple path from S to T in a directed graph so that the product of its weights is maximum

I'm looking for an algorithm that finds a simple path from S to T in a directed graph (which might have cycles) so that the product of edge weights in the path is maximum. All the edge weights of the ...
• 133
45 views

### Is there a name for a directed graph where we cannot re-enter a vertex that we leave (to a different vertex)?

I am wondering if there is an "official" name for a directed graph where we cannot re-enter a vertex once we leave it to a different vertex. Here's an example of one such graph, where once ...
63 views

### Edmond's theorem for k-disjoint arborescences in digraphs

Recently while studying arborescences in graph theory, I came across Edmond's theorem for $k$ edge-disjoint arborescences in digraphs if a finite digraph is $k$ edge-connected from a vertex r for ...
543 views

### Find all nodes in directed graph from starting node that complete a loop

Suppose I have a directed graph, where one of the nodes is selected to be the "initial" node. What algorithms should I consider using to to find all the nodes that have a path from the ...
• 101
160 views

### Find most vertices in a directed tree where no path of length less than 3 connects any pair

Given a directed tree $T = (V, E)$, we need to find a set of vertices $A \subseteq V$ such that for every two vertices $v,u \in A$ either there is no path between them or the path between them is of ...
• 449
1 vote
508 views

### How to find lightest path in directed weighted graph where each edge has a color

We're Given a directed graph $G = (V, E)$ and a weight function $\omega : E \rightarrow \mathbb{Z}$. Each edge is colored with one of these colors: Red, Green, Blue. Given two vertices $s,t \in V$, ...
• 449
33 views

### Symmetry group of the acyclic oriented L-cube using the Hyperoctahedral group

I'm trying to figure out all elements of a symmetry group for the acyclic oriented $L$-cube. I do have an algorithm, but its complexity is not suitable for larger $L$. I computed $L=5$ on my old ...
• 51
126 views

### Find the directed subgraph with least edges that preserves connectivity

I have a directed graph $G$ with a set of nodes $N$ and a set of edges $E$ with the following property : if $(A\to B)\in E$ and $(B\to C)\in E$, then $(A\to C)\in E$, for all nodes $A,B,C$. I would ...
1 vote
123 views

### Is the first distance that gets assigned to a node in BFS always the shortest distance?

Consider the following bfs pseudo code that calculates distances of all nodes from $s$ in graph $G=(V,E)$. I know that if $G$ was undirected and unweighted, then the above bfs would calculate correct ...
• 113
458 views

### Shortest walk with alternating colors in a directed graph

Let $G$ be a directed graph such that every edge is colored (red, yellow or green). I want to compute the shortest walk (possibly with repeated vertices) with the restriction that the colors are ...
• 115
489 views

### Connectivity in Directed Graph

Connectivity in undirected graph can be easily identified using Disjoint Union Set (Union Find). Is there any way to check connectivity in a directed graph efficiently other than doing Depth First ...
938 views

### Maximum number of distinct nodes that can be visited on a single walk

Given a directed graph which may contain cycles, how can I find the maximum number of distinct nodes that can be visited on a single walk? I have done some research and the most similar-sounding ...
• 133
162 views

### Iterative version of depth-first-search code to detect cycle in a directed graph [duplicate]

I have solved a problem that required me to find if the given directed graph had a cycle or not. The deal is, I used a recursive approach to solve it in the depth-first-search method. I was just ...
41 views

### Given a vertex in a digraph, is there a standard term for (the vertices reachable from it) union (the vertices reaching it)?

Question in title. Looking for whether there is a term that is, if not widely understood, at least citeable to a source. This is equivalent to asking for the set of nodes that are comparable to the ...
• 3,523
1 vote
244 views

### Minimal cut of a directed graph such that disjoint elements are strongly connected

Given an arbitrary directed graph $G$ (which may not necessarily be connected) find a minimum set of edges $S\subseteq E$ such that every disjoint component of $G(V,E\cap S')$ is strongly connected. A ...
97 views

### Find two paths in a Graph which are disjunct in

Assuming we have two trains that start in one source edge. I want to find an algorithm that finds two paths for these trains so that they won't meet in an edge at any given time. So we have the train ...
233 views

### How to find long trails in a multidigraph

I have a directed multigraph (a multigraph is a graph that can have more than one edge between any two nodes). In Wikipedia's terminology, this is a directed multigraph (edges without own identity). I ...
• 201
1k views

### Find palindrome in directed Graph where edges are either blue or red

This is the given task: Suppose you are given an arbitrary directed graph G in which each edge is colored either red or blue, along with two special vertices s and t. Describe an algorithm that either ...
376 views

### DAG: When adding an edge that would normally result in a cycle, is there an algorithm to split the graph instead?

Summary I am using a DAG to compress a tree structure with many repeated nodes (the repeated nodes only very seldomly do not also have repeated edges out.) Normally, when attempting to add an edge to ...
68 views

### Is this a variant of "Path Covering"?

According to 1, "a path cover of a directed graph G is a set of disjoint paths in G which together contain all the vertices of G". In my research, I met a similar problem. There, you can add ...
• 259
74 views

### Transitive closure of a directed graph (reachability) algorithm intuition/explanation

Consider $n\times n$ matrix $T$ which represents transitive closure of a directed graph. That means $T_{uv}=1$ if and only if there exist a directed path between vertices $u$ and $v$. Initially, $T$ ...
41 views

### Walks on Directed graphs

Let G = (V,E) be a directed graph, where V is a finite set of nodes, and E ⊆ V × V be the set of (directed) edges (arcs). In particular, we identify a node as the initial node, and a node as the final ...
1 vote
591 views

### Longest path in a strongly connected component

So if we assume that we have some strongly connected component G with n vertices. I would like to find the length of the longest path in that component. My idea is: In a strongly connected component ...
• 27
488 views

### Finding shortest path for DAG using dynamic programming vs topological sort?

Why is it that when I read about finding the shortest path for a DAG I usually just hear about topological sort? Why not use dynamic programming where the shortest path to a vertex is simply the ...
• 153
362 views

### Given an undirected graph, find an orientation such that every vertex has out-degree at least 3

Given an undirected graph $G=(V,E)$, describe an algorithm that computes an orientation of $E$ such that each vertex has out-degree at least 3. I know how to check if a vertex $v$ has at least $k$ ...
• 241