# Multistage Vertex Cover

@inproceedings{Fluschnik2019MultistageVC, title={Multistage Vertex Cover}, author={Till Fluschnik and Rolf Niedermeier and Valentin Rohm and Philipp Zschoche}, booktitle={IPEC}, year={2019} }

Covering all edges of a graph by a small number of vertices, this is the NP-complete Vertex Cover problem. It is among the most fundamental graph-algorithmic problems. Following a recent trend in studying temporal graphs (a sequence of graphs, so-called layers, over the same vertex set but, over time, changing edge sets), we initiate the study of Multistage Vertex Cover. Herein, given a temporal graph, the goal is to find for each layer of the temporal graph a small vertex cover and to… Expand

#### 15 Citations

Multistage Problems on a Global Budget

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2021

This work studies the different (time) layers of a temporal graph, and finds that sometimes the global multistage versions of NP-hard problems such as Vertex Cover turn out to be computationally easier than the ones of polynomial-time solvable problemssuch as Matching. Expand

Sliding window temporal graph coloring

- Computer Science
- J. Comput. Syst. Sci.
- 2021

A thorough investigation of the computational complexity of this temporal coloring problem is presented, and strong computational hardness results are proved, complemented by efficient exact and approximation algorithms. Expand

Sliding Window Temporal Graph Coloring

- Computer Science, Mathematics
- AAAI
- 2019

A thorough investigation of the computational complexity of this temporal coloring problem is presented, and strong computational hardness results are proved, complemented by efficient exact and approximation algorithms. Expand

A General Approach to Approximate Multistage Subgraph Problems

- Computer Science
- ArXiv
- 2021

This work presents a framework that provides a (1/ √ 2χ)-approximation algorithm for the 2-stage restriction of an MSP if the similarity of subsequent solutions is measured as the intersection cardinality and said MSP is preficient, i.e., the authors can efficiently find a single-stage solution that prefers some given subset. Expand

LP-based algorithms for multistage minimization problems

- Computer Science, Mathematics
- WAOA
- 2020

A new two-threshold rounding scheme, tailored for multistage problems, is introduced and it is shown that this rounding scheme gives a 2$f$-approximation algorithm for the multistages variant of the f-Set Cover problem, where each element belongs to at most f sets. Expand

Approximating Multistage Matching Problems

- Computer Science
- IWOCA
- 2021

It is shown that multistage perfect matching problems are NP-hard even in very restricted scenarios, and new approximation algorithms and methods are proposed to transfer results between different problem variants without loosing approximation guarantees. Expand

A Multistage View on 2-Satisfiability

- Computer Science, Mathematics
- CIAC
- 2021

It is proved that Multistage 2-SAT is NP-hard even in quite restricted cases and parameterized algorithms for Multistages are presented and proved to be asymptotically optimal. Expand

Parameterized Algorithms for Diverse Multistage Problems

- Computer Science
- ESA
- 2021

This work introduces a framework allowing it to prove that a number of diverse multistage problems are fixed-parameter tractable by diversity, namely Perfect Matching, s-t Path, Matroid Independent Set, and Plurality Voting. Expand

Multistage Committee Election

- Mathematics, Computer Science
- ArXiv
- 2020

Two time-dependent multistage models based on simple Plurality voting are introduced and it is proved that being revolutionary seems to be "easier" than being conservative, and that the conservative model remains NP-hard while the revolutionary model becomes polynomial-time solvable. Expand

As Time Goes By: Reflections on Treewidth for Temporal Graphs

- Computer Science
- Treewidth, Kernels, and Algorithms
- 2020

Fresh algorithmic views on temporal tree decompositions and temporal treewidth are discussed, some of the recent work is reviewed together with some encountered pitfalls, and challenges for future research are pointed out. Expand

#### References

SHOWING 1-10 OF 33 REFERENCES

Temporal Vertex Cover with a Sliding Time Window

- Computer Science, Mathematics
- ICALP
- 2018

This paper introduces and study two natural temporal extensions of the classical problem VERTEX COVER, and presents a thorough investigation of the computational complexity and approximability of these two temporal covering problems. Expand

Temporal vertex cover with a sliding time window

- Computer Science
- J. Comput. Syst. Sci.
- 2020

This paper introduces and study two natural temporal extensions of the classical problem VERTEX COVER and presents a thorough investigation of the computational complexity and approximability of these two temporal covering problems. Expand

Incremental list coloring of graphs, parameterized by conservation

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2013

It is shown that even on bipartite graphs the problem is NP-hard for k>=3 and W[1]-hard for an unbounded number of colors when parameterized by c, and fixed-parameter tractability for the combined parameter treewidth and number k of colors is shown. Expand

Some Simplified NP-Complete Graph Problems

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 1976

This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete. Expand

Temporal Graph Classes: A View Through Temporal Separators

- Computer Science, Mathematics
- WG
- 2018

This work investigates the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph and identifies sharp borders between tractable and intractable cases. Expand

Vertex Cover Reconfiguration and Beyond

- Computer Science, Mathematics
- ISAAC
- 2014

It is shown that VCR remains w[1]-hard on bipartite graphs, is NP-hard but fixed-parameter tractable on (regular) graphs of bounded degree, and is solvable in polynomial time on trees and (with some additional restrictions) on cactus graphs. Expand

Multistage Matchings

- Computer Science
- SWAT
- 2018

14 We consider a multistage version of the Perfect Matching problem which models the 15 scenario where the costs of edges change over time and we seek to obtain a solution that achieves 16 low total… Expand

On the parameterized complexity of dynamic problems

- Mathematics, Computer Science
- Theor. Comput. Sci.
- 2015

A study of the dynamic versions of a number of problems including Vertex cover, Maximum Clique, Connected Vertex Cover and Connected Dominating Set, and introduces the reoptimization parameter, which bounds the difference between the cardinalities of initial and target solutions. Expand

Maximum independent sets in 3- and 4-regular Hamiltonian graphs

- Computer Science, Mathematics
- Discret. Math.
- 2010

This paper shows that the independent set problem for 3-regular Hamiltonian planar graphs is NP-complete, and shows that this problem is also NP- complete for smooth 4- regular Hamiltonian graphs. Expand

Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams

- Computer Science, Mathematics
- SODA
- 2016

This paper presents a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams, and considers a larger family of parameterized problems for which this primitive yields fast, small-space dynamic graph stream algorithms. Expand