XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure

Bodlaender, Hans L.; Groenland, Carla; Jacob, Hugo

doi:10.48550/arxiv.2201.13119

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Undirected Flow With Lower Bounds ([23 Problem Nd37])1

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2022

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“…Our proof that UFLB is XNLP-hard for pathwidth is by reduction from Accepting Non-deterministic Checking Counter Machine from [11]. XNLP-completeness of CDS for pathwidth was shown in [10,Thm. 8].…”

Section: Undirected Flow With Lower Bounds ([23 Problem Nd37])mentioning

confidence: 96%

Problems Hard for Treewidth but Easy for Stable Gonality

Bodlaender

Cornelissen

Wegen

2022

Lecture Notes in Computer Science

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We show that some natural problems that are XNLPhard (hence W[t]-hard for all t) when parameterized by pathwidth or treewidth, become FPT when parameterized by stable gonality, a novel graph parameter based on optimal maps from graphs to trees. The problems we consider are classical flow and orientation problems, such as Undirected Flow with Lower Bounds, Minimum Maximum Outdegree, and capacitated optimization problems such as Capacitated (Red-Blue) Dominating Set. Our hardness claims beat existing results. The FPT algorithms use a new parameter "treebreadth", associated to a weighted tree partition, as well as DP and ILP.

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Section: Undirected Flow With Lower Bounds ([23 Problem Nd37])mentioning

confidence: 96%