Flows on hypergraphs

@article{Cambini1997FlowsOH,
  title={Flows on hypergraphs},
  author={Riccardo Cambini and Giorgio Gallo and Maria Grazia Scutell{\`a}},
  journal={Mathematical Programming},
  year={1997},
  volume={78},
  pages={195-217}
}
We consider the capacitated minimum cost flow problem on directed hypergraphs. We define spanning hypertrees so generalizing the spanning tree of a standard graph, and show that, like in the standard and in the generalized minimum cost flow problems, a correspondence exists between bases and spanning hypertrees. Then, we show that, like for the network simplex algorithms for the standard and for the generalized minimum cost flow problems, most of the computations performed at each pivot… 

A Hypergraph Network Simplex Algorithm

A network simplex algorithm for the minimum cost flow problem on graph-based hypergraphs which are directed hyper graphs of a particular form occurring in railway rotation planning and it is shown that most operations of thesimplex algorithm can be done combinatorially by exploiting the underlying digraph structure.

SPANNING HYPERFOREST OF A HYPERGRAPH

We are interested in the complexity of a problem involving spanning hyperforests (a union of hypertrees, which covers all of the vertices) of a $k$-hypergraph. We describe the relevant definitions

Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach

A specific dynamic problem which finds several interesting applications, especially in the framework of knowledge representation: the maintenance of minimum weight hyperpaths under hyperarc weight increases and hyperarc deletions is addressed: a new efficient algorithm applicable for a wide class of hyperpath weight measures.

Max Horn SAT and the minimum cut problem in directed hypergraphs

This paper considers the Maximum Horn Satisfiability problem, which is reduced to the problem of finding a minimum cardinality cut on a directed hypergraph, and proposes different IP formulations, related to three different definitions of hyperpath weight.

Finding (s, d)-Hypernetworks in F-Hypergraphs is NP-Hard

This work considers the problem of computing an (s, d)-hypernetwork in an acyclic Fhypergraph, and finds that for acyClic F hypergraphs the problem is NP-hard, which also implies the issue is hard in BFhypergraphs.

Decremental Maintenance of Reachability in Hypergraphs and Minimum Models of Horn Formulae

A decremental algorithm for maintaining minimum rank hyperpaths in a directed hypergraph from a source vertex s to all other vertices, under the assumption of unit hyperedge weights.

Directed hypergraphs: Introduction and fundamental algorithms - A survey

A Spectral Framework for a Class of Undirected Hypergraphs

It is claimed that undirected hypergraphs open the way to solve new learning tasks and model new problems based on set similarity or dominance, and is currently exploring applications for modeling games between teams and for graph summarization.

The Image Containment Problem and Some Classes of Polynomial Instances

A family of nontrivial ICP instances, called worst case demand (WCD) instances, are studied and it is proved that such instances can be recognized and solved in polynomial time via linear programming.

References

SHOWING 1-10 OF 19 REFERENCES

Gainfree Leontief substitution flow problems

In a survey of applications, it is shown how the Leontief flow paradigm links polyhedral combinatorics, expert systems, mixed integer model formulation, and some problems in graph optimization.

Graph Algorithms for Functional Dependency Manipulation

A graph-theoretic approach for the representation of functional dependenoes in relauonal databases is introduced and applied in the construction of algorithms for manipulating dependencies, which leads to simpler proofs and, in some cases, more efficient algorithms than in the current literature.

Extreme points of leontief substitution systems

Algorithms for network programming

Network Flows: Theory, Algorithms, and Applications

Directed Hypergraphs and Applications

Minimum Cost Flows on Hypergraphs

Here it is shown how the simplex operations can be specialized in order to exploit the structure of the problem, and defines spanning hypertrees of a hypergraph so generalizing the spanning tree of a standard graph, and shows that a correspondence exists between bases and spanning hypertree.