# Efficient reassembling of three-regular planar graphs

@article{Kfoury2020EfficientRO, title={Efficient reassembling of three-regular planar graphs}, author={Assaf J. Kfoury and Benjamin Sisson}, journal={Journal of Combinatorial Optimization}, year={2020}, volume={39}, pages={1153-1207} }

A reassembling of a simple graph $$G = (V,E)$$ G = ( V , E ) is an abstraction of a problem arising in earlier studies of network analysis (Bestavros and Kfoury, in: Proceedings of IFIP working conference on domain-specific 1640 languages (DSL 2011), EPTCS volume 66, 2011; Kfoury, in: Proceedings of SBLP 2011: Brazilian symposium on programming; Kfoury, in Sci Comput Program 93(Part A):19–38; Soule et al., in: Proceedings of 4th international workshop on equation-based object oriented modeling… Expand

#### Figures and Topics from this paper

#### 2 Citations

A Fixed-Parameter Linear-Time Algorithm to Compute Principal Typings of Planar Flow Networks

- Computer Science
- ArXiv
- 2018

This work presents an alternative and simpler method for computing principal typings of flow networks in fixed-parameter linear-time -- where the parameter not to be exceeded is what is called the edge-outerplanarity of the networks' underlying graphs. Expand

A Fixed-Parameter Linear-Time Algorithm for Maximum Flow in Planar Flow Networks

- Mathematics, Computer Science
- ArXiv
- 2018

This work pulls together previously established graph-theoretical results to produce the algorithm in the paper's title, which is based on three easy elementary lemmas. Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Efficient reassembling of graphs, part 1: the linear case

- Mathematics, Computer Science
- J. Comb. Optim.
- 2017

The particular case of linear reassembling, which requires that the next edge to be spliced must be adjacent to an already spliced edge, is examined, and it is proved that the known NP-hardness of CutWidth and MinArr imply the NP- hardness of α-optimization and β-optimism. Expand

Efficient Reassembling of Graphs, Part 2: The Balanced Case

- Computer Science, Mathematics
- ArXiv
- 2016

The two main results in this report are the NP-hardness of alpha-optimization and beta- Optimization of balanced reassembling of graphs. Expand

Constructive Linear Time Algorithms for Small Cutwidth and Carving-Width

- Mathematics, Computer Science
- ISAAC
- 2000

A constructive proof of the fact that both the Graph Minor series of Robertson and Seymour imply and the algorithms of this proof are optimal and able to output the corresponding pair (T, χ) in case of an affirmative answer are given. Expand

Disjoint paths in sparse graphs

- Computer Science, Mathematics
- Discret. Appl. Math.
- 2009

Thek-edge-outerplanar graphs are introduced, a class of planar graphs with arbitrary (but bounded) tree-width that generalizes the cacti, and it is shown that the integrality gap of the maximum edge-disjoint paths problem is bounded in these graphs. Expand

Why Should Biconnected Components be Identified First

- Computer Science, Mathematics
- Discret. Appl. Math.
- 1993

It is shown here that for several graph optimization problems, including the weighted vertex cover and the independent set problems, it suffices to know how to solve the problem on each biconnected component of the graph. Expand

Call routing and the ratcatcher

- Mathematics, Computer Science
- Comb.
- 1994

It follows that branch-width is polynomially computable for planar graphs—that too is NP-hard for general graphs. Expand

Determining the Smallest k Such That G Is k -Outerplanar

- Mathematics, Computer Science
- ESA
- 2007

A linear-time 4-approximation algorithm for the outerplanarity index is given and it is shown how it can be used to solve maximum independent set and several other NP-hard problems faster on planar graphs with outerplanularity index within a constant factor of their treewidth. Expand

Algorithm 447: efficient algorithms for graph manipulation

- Computer Science, Mathematics
- CACM
- 1973

Efficient algorithms are presented for partitioning a graph into connected components, biconnected components and simple paths and each iteration produces a new path between two vertices already on paths. Expand

Optimal branch-decomposition of planar graphs in O(n3) Time

- Mathematics, Computer Science
- TALG
- 2008

An O(n) time algorithm for constructing a minimum-width branch-decomposition of a given planar graph with n vertices is given through a refinement to the previously best known algorithm of Seymour and Thomas. Expand

Planarity Testing and Embedding

- Mathematics, Computer Science
- Handbook of Graph Drawing and Visualization
- 2013

A comparison of the Lempel-Even-Cederbaum Algorithm with the Shih-Hsu Algorithm and the Boyer-Myrvold Algorithm shows that the former is more efficient while the latter is less efficient than the latter. Expand