Approximating Multistage Matching Problems

Chimani, Markus; Troost, Niklas; Wiedera, Tilo

doi:10.1007/s00453-022-00951-x

Cited by 6 publications

(1 citation statement)

References 23 publications

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“…Typically, the solutions are sets of vertices or edges, and the amount of change is measured with the symmetric difference of the sets. Many combinatorial problems have been studied in the multistage setting including matching problems [35,60,61], vertex cover [62], finding paths [63], 2-coloring [64], and others [65][66][67][68][69].…”

Section: Related Workmentioning

confidence: 99%

Cluster Editing for Multi-Layer and Temporal Graphs

Molter

Sorge

Suchý

2023

Preprint

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Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same vertex set, called layers and aim to transform all layers into cluster graphs (disjoint unions of cliques) that differ only slightly. More specifically, we want to mark at most d vertices and to transform each layer into a cluster graph using at most k edge additions or deletions per layer so that, if we remove the marked vertices, we obtain the same cluster graph in all layers. In Temporal Cluster Editing we receive a sequence of layers and we want to transform each layer into a cluster graph so that consecutive layers differ only slightly. That is, we want to transform each layer into a cluster graph with at most k edge additions or deletions and to mark a distinct set of d vertices in each layer so that each two consecutive layers are the same after removing the vertices marked in the first of the two layers. We study the combinatorial structure of the two problems via their parameterized complexity with respect to the parameters d and k, among others. Despite the similar definition, the two problems behave quite differently: In particular, Multi-Layer Cluster Editing is fixed-parameter tractable with running time kO(k+d) sO(1) for inputs of size s, whereas Temporal Cluster Editing is W[1]-hard with respect to k even if d = 3.

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Section: Related Workmentioning

confidence: 99%

Cluster Editing for Multi-Layer and Temporal Graphs

Molter

Sorge

Suchý

2023

Preprint

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Cluster Editing for Multi-Layer and Temporal Graphs

Chen,

Molter,

Sorge

et al. 2024

Theory Comput Syst

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Approximating Multistage Matching Problems

2022

Self Cite

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In multistage perfect matching problems, we are given a sequence of graphs on the same vertex set and are asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as possible. More precisely, we aim to maximize the intersections, or minimize the unions between consecutive matchings. We show that these problems are NP-hard even in very restricted scenarios. As our main contribution, we present the first non-trivial approximation algorithms for these problems: On the one hand, we devise a tight approximation on graph sequences of length two (2-stage graphs). On the other hand, we propose several general methods to deduce multistage approximations from blackbox approximations on 2-stage graphs.

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Approximating Multistage Matching Problems

Cited by 6 publications

References 23 publications

Cluster Editing for Multi-Layer and Temporal Graphs

Cluster Editing for Multi-Layer and Temporal Graphs

Cluster Editing for Multi-Layer and Temporal Graphs

Approximating Multistage Matching Problems

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