# Tagged Questions

Questions about graphs, discrete structures of nodes which are connected by edges. Popular flavors are trees and networks with edge capacity.

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### Minimal hypergraph transversals

the exact complexity for hypergraph transversal problem is yet unknown and is an open research problem. However, I would need a fast way to compute, on paper, the minimal transversal of a hypergraph. ...
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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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### Is is possible compute the max flow with max cost through an instance of maxflow-mincost?

I have a flow network with gains. In practical terms, a gain is the opposite of a cost. So, I interested in finding the maximal gain of a network flow, what could be interpreted as finding a maximum ...
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### Powerlaw graphs : Number of hubs and fraction of edges incident on them

As per the definition of power law, the fraction P(k) of nodes with k degree for large values of k , given by P(k) ~k ^-r . In this definition, the term large value is not clearly defined. Does ...
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### Orient edges in a mixed graph to minimize the critical path

A mixed graph is a graph that has directed and undirected edges. Is there an efficient algorithm that allows the orientation of undirected edges in a mixed graph in such a way that no cycle is ...
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### Computing maximum-cost subtree that uses at most k edges

I'm looking for an efficient algorithm for the following problem: Input: a binary, complete tree with a cost on each edge, an integer $k$ Output: the maximum-cost subtree containing $\le k$ edges ...
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### Single-source shortest path algorithm for graphs representing stacked behavior

I am trying to compute a single-source shortest path in an interprocedural control flow graph (iCFG). That is a directed, unweighted, cyclic graph with edge labels. Some of these labels represent ...
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### Can we create the level graph from sink to source in Dinitz?

One of the steps of the Dinitz algorithm for computing maximal flows is to create a level graph. It is created from source to sink using BFS. Could we create the level graph from sink to source ...
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### Checking for 4-cycles in a graph

I was reviewing some selected problems on algorithms and time complexity and the notes had the following exercise (ex. 4.3 from book Algorithms by Dasgupta, Vazirani, Papadimitriou): Design and ...
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### Complete set of basic circuits for McLane's Theorem

I was assigned a project in which i had to implement some algorithms concerning graphs. The last one is the one described in the title. I have to make an algorithm that uses McLane's theorem (https://...
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### Counting specific subgraphs

For a given undirected graph G, I want to count all the subgraphs H that satisfies the following conditions: H.V = G.V (The subgraph will containt all the original graph nodes) H is connected (...
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### Is finding all cycles in a graph using some version of Johnson's algorithm (code provided) really polynomial (benchmark provided)?

This is the algorithm I'm using: http://stackoverflow.com/questions/12367801/finding-all-cycles-in-undirected-graphs/14115627#14115627 Specifically C#, but the linked thread has numerous languages. ...
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### Is there a minimum spanning tree including $e$ after removing at most $k$ edges?

Let an undirected, connected graph $G=(V,E)$ with the weight funciton $w:E\to \mathbb{R}$, an edge $e$, and $0<k\in\mathbb{N}$. Describe an algorithm determines if there are at most $k$ edges could ...
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### What is the difference in 'logical array blocked' and array list B, and what do they represent?

In Johnson's 1975 Paper 'Finding All the Elementary Circuits of a Directed Graph', his psuedocode refers to two separate data structures, logical array blocked and list array B. What is the difference ...
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### Why is bipartite graph matching hard?

I am reading on how solving maximum flow (Ford-Fulkerson) can be also used to solve unweighted bipartite graph matching problem. I think I don't understand the essence of this problem, because to me ...
I want an algorithm that takes the following Input: $M,N,k,d$ positive integers such that $kM = dN$. and produces the following Output: Random bipartite graph, with $M$ vertices all of degree $k$ ...