Multistage Vertex Cover

Fluschnik, Till; Niedermeier, Rolf; Rohm, Valentin; Zschoche, Philipp

doi:10.4230/lipics.ipec.2019.14

Cited by 11 publications

(9 citation statements)

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“…Related work. Our model follows the recently proposed multistage model [7,15], that led to several multistage problems [2,3,10,11] next to ours. Graph problems considered in the multistage model often study classic problems on temporal graphs (a sequence of graphs over the same vertex set).…”

Section: Introductionmentioning

confidence: 99%

Multistage Committee Election

Bredereck,

Fluschnik,

Kaczmarczyk

2020

Preprint

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Electing a single committee of a small size is a classical and well-understood voting situation. Being interested in a sequence of committees, we introduce and study two time-dependent multistage models based on simple Plurality voting. Therein, we are given a sequence of voting profiles (stages) over the same set of agents and candidates, and our task is to find a small committee for each stage of high score. In the conservative model we additionally require that any two consecutive committees have a small symmetric difference. Analogously, in the revolutionary model we require large symmetric differences. We prove both models to be NP-hard even for a constant number of agents, and, based on this, initiate a parameterized complexity analysis for the most natural parameters and combinations thereof. Among other results, we prove both models to be in XP yet W[1]-hard regarding the number of stages, and that being revolutionary seems to be "easier" than being conservative: If the (upper-resp. lower-) bound on the size of symmetric differences is constant, the conservative model remains NP-hard while the revolutionary model becomes polynomial-time solvable.

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Section: Introductionmentioning

confidence: 99%

Multistage Committee Election

Bredereck,

Fluschnik,

Kaczmarczyk

2020

Preprint

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“…P in each stage. Most common choices for transition qualities are symmetric difference cost (q (S i , S i+1 ) := |S i S i+1 | with Ψ = min; see, e.g., [1,4,5,[9][10][11]15]) and intersection profit (q ∩ (S i , S i+1 ) := |S i ∩ S i+1 | with Ψ = max; see, e.g., [2,3,6,11]).…”

Section: Definition 2 (Multistage Subgraph Problem) a Multistage Subg...mentioning

confidence: 99%

“…In many cases, generalizing a polynomial-time solvable problem to a multistage setting renders it NP-hard (e.g., Multistage Shortest s-t-Path [11] or Multistage Perfect Matching [15]). There is some work on identifying parameters that allow for fixed-parameter tractability of NP-hard multistage problems [5,[9][10][11]16]. Another popular approach to tackle such problems are approximation algorithms [1][2][3][4]8].…”

Section: Introductionmentioning

confidence: 99%

A General Approach to Approximate Multistage Subgraph Problems

Chimani¹,

Troost²,

Wiedera³

2021

Preprint

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In a Subgraph Problem we are given some graph and want to find a feasible subgraph that optimizes some measure. We consider Multistage Subgraph Problems (MSPs), where we are given a sequence of graph instances (stages) and are asked to find a sequence of subgraphs, one for each stage, such that each is optimal for its respective stage and the subgraphs for subsequent stages are as similar as possible.We present 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., we can efficiently find a single-stage solution that prefers some given subset. The approximation factor is dependent on the instance's intertwinement χ, a similarity measure for multistage graphs.We also show that for any MSP, independent of similarity measure and preficiency, given an exact or approximation algorithm for a constant number of stages, we can approximate the MSP for an unrestricted number of stages.Finally, we combine and apply these results and show that the above restrictions describe a very rich class of MSPs and that proving membership for this class is mostly straightforward. As examples, we explicitly state these proofs for natural multistage versions of Perfect Matching, Shortest s-t-Path, Minimum s-t-Cut and further classical problems on bipartite or planar graphs, namely Maximum Cut, Vertex Cover, Independent Set, and Biclique.

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“…Related Work. Independent Set remains NP-complete on 3-and 4-regular Hamiltonian graphs [7], which enabled to prove NP-hardness for a temporal graph problem with two layers [8].…”

Section: Hamiltonian Planar ≤ 3-regularmentioning

confidence: 99%

Feedback Vertex Set on Hamiltonian Graphs

Cavallaro¹,

Fluschnik²

2021

Preprint

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We study the computational complexity of Feedback Vertex Set on subclasses of Hamiltonian graphs. In particular, we consider Hamiltonian graphs that are regular or are planar and regular. Moreover, we study the less known class of p-Hamiltonianordered graphs, which are graphs that admit for any p-tuple of vertices a Hamiltonian cycle visiting them in the order given by the tuple. We prove that Feedback Vertex Set remains NP-hard in these restricted cases, even if a Hamiltonian cycle is additionally given as part of the input.

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Multistage Vertex Cover

Cited by 11 publications

References 0 publications

Multistage Committee Election

Multistage Committee Election

A General Approach to Approximate Multistage Subgraph Problems

Feedback Vertex Set on Hamiltonian Graphs

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