Why is “topological sorting” topological?
Why is “topological sorting” called “topological”? Is it just because it determines an order without altering any vertices or edges — like a doughnut and coffee cup are topologically equivalent? Why is...
View ArticleRealization 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...
View ArticleIndexing structure for all-pairs min-cuts in a huge DAG
I have a huge DAG – e.g., the dependency graph of all packages in a linux distribution. Suppose I’d like to make a user-friendly tool that makes it very easy to understand how to break the transitive...
View ArticleK-path cover problem for a DAG
I am doing a little literature review and I was trying to know if, for a directed acyclic graph, the minimum k-path cover problem is solvable in polynomial time. A k-path cover is a set of paths with...
View ArticleAn edge orientation procedure to generate all acyclic orientations of a graph
Consider the following scheme for enumerating acyclic digraphs (DAGs) by orienting the edges in an undirected graph $G$ with $n = ||V||$ vertices: (1) Generate all $n!$ possible permutations $p_i$ of...
View ArticleWhat does the contention-free communication assumption really mean in the...
In many papers about DAG (directed-acyclic graph) scheduling in distributed systems, the authors make the assumption that the communication between the processors of the system where the DAG is...
View ArticleClik here to view.
Shortest path in DAG with path dependent arc costs
I’ve got the following problem Consider a DAG $G=(V,E)$ with $V=[v_1,…,v_n]$, and edge-set $E=[e_1,…,e_m]$, with associated costs $c_1,…,c_m$. The problem is to find the shortest paths from an initial...
View ArticleWhen does a graph admit an orientation in which there is at most one s-t walk?
Consider the following problem: Input: a simple (undirected) graph $G=(V,E)$. Question: Is there an orientation of $G$ satisfying the property that for every $s,t in V$ there is at most one (directed)...
View ArticleLongest path in a DAG that's not too long
The problem I am interested in is a simple variant of the longest path problem on DAGs: find a path between two chosen vertices in a DAG such that the sum of the weights of its constituent edges is...
View ArticleReference for mixed graph acyclicity testing algorithm?
A mixed graph is a graph that may have both directed and undirected edges. Its underlying undirected graph is obtained by forgetting the orientations of the directed edges, and in the other direction...
View ArticleIs there a linear-time algorithm for max flow on dags
What is the fastest known algorithm for max flow on dags? Can there be a linear-time algorithm running in time $O(|V|+|E|)$? Input: a weighted dag $G=(V,E,w)$ where $E$ is given as an edge list $E$ and...
View ArticleLexicographically minimal topological sort of a labeled DAG
Consider the problem where we are given as input a directed acyclic graph $G = (V, E)$, a labeling function $lambda$ from $V$ to some set $L$ with a total order $<_L$ (e.g., the integers), and where...
View ArticleLongest path in a DAG that's not too long
The problem I am interested in is a simple variant of the longest path problem on DAGs: find a path between two chosen vertices in a DAG such that the sum of the weights of its constituent edges is...
View Article
