# Edge-Disjoint Branchings in Temporal Graphs

@article{Campos2020EdgeDisjointBI, title={Edge-Disjoint Branchings in Temporal Graphs}, author={Victor A. Campos and Raul Lopes and Andrea Marino and Ana Silva}, journal={Combinatorial Algorithms}, year={2020}, volume={12126}, pages={112 - 125} }

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## 4 Citations

### Menger's Theorem for Temporal Paths (Not Walks)

- MathematicsArXiv
- 2022

A temporal graph is a graph whose edges are available only at speciﬁc times. In this scenario, the only valid walks are the ones traversing adjacent edges respecting their availability, i.e. sequence…

### Mengerian graphs: characterization and recognition

- MathematicsArXiv
- 2022

A temporal graph G is a graph that changes with time. More specif-ically, it is a pair ( G, λ ) where G is a graph and λ is a function on the edges of G that describes when each edge e ∈ E ( G ) is…

### Combinatorial Algorithms: 31st International Workshop, IWOCA 2020, Bordeaux, France, June 8–10, 2020, Proceedings

- Computer ScienceIWOCA
- 2020

This paper presents a meta-modelling architecture suitable for large-scale distributed Optimization Via Population Protocols and some examples show how this architecture can be implemented in the rapidly changing environment.

## References

SHOWING 1-10 OF 29 REFERENCES

### Temporal Flows in Temporal Networks

- Mathematics, Computer ScienceCIAC
- 2017

The flow model is new and differs from the “flows over time” model, also called “dynamic flows” in the literature, and it is shown that the problem of finding the maximum amount of flow that can pass from a source vertex to a sink vertex up to a given time is solvable in Polynomial time.

### Temporal Network Optimization Subject to Connectivity Constraints

- Computer Science, MathematicsAlgorithmica
- 2018

This work gives two efficient algorithms for computing shortest time-respecting paths on a temporal network, and proves that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks.

### Connectivity and inference problems for temporal networks

- Mathematics, Computer ScienceSTOC '00
- 2000

This work defines and studies the class of inference problems, in which it seeks to reconstruct a partially specified time labeling of a network in a manner consistent with an observed history of information flow, and provides results on two types of problems for temporal networks.

### The complexity of satisfiability problems

- MathematicsSTOC
- 1978

An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.

### An Introduction to Temporal Graphs: An Algorithmic Perspective*

- Computer ScienceInternet Math.
- 2016

This paper surveys here recent results on temporal graphs and temporal graph problems that have appeared in the Computer Science community and urges the development of a temporal extension of graph theory.

### Path Problems in Temporal Graphs

- Computer ScienceProc. VLDB Endow.
- 2014

The shortcomings of classic shortest path in a temporal graph are shown, various concepts of "shortest" path for temporal graphs are studied, and efficient algorithms to compute these temporal paths are proposed.

### Vulnerability of scheduled networks and a generalization of Menger's Theorem

- MathematicsNetworks
- 1996

An edge-scheduled network N is a multigraph G = (V, E), where each edge e ϵ E has been assigned two real weights: a start time α(e) and a finish time β(e). Such a multigraph models a communication or…

### Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2010

This work shows that the edge-disjoint paths problem is W[1]-hard, and it is shown that the problem remains W[ 1]-hard even if the demand graph consists of two sets of parallel edges.

### Time-varying graphs and dynamic networks

- Computer ScienceInt. J. Parallel Emergent Distributed Syst.
- 2012

This paper presents a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature, and examines how TVGs can be used to study the evolution of network properties, and proposes different techniques, depending on whether the indicators for these properties are atemporal or temporal.

### Stream graphs and link streams for the modeling of interactions over time

- Computer ScienceSocial Network Analysis and Mining
- 2018

This paper generalizes graph concepts to cope with both intrinsically temporal and structural nature of interactions, and obtains a language to directly deal with interactions over time, similar to the language provided by graphs to deal with relations.