DeepAI

# Parameterized Complexity of Minimum Membership Dominating Set

Given a graph G=(V,E) and an integer k, the Minimum Membership Dominating Set (MMDS) problem seeks to find a dominating set S ⊆ V of G such that for each v ∈ V, |N[v] ∩ S| is at most k. We investigate the parameterized complexity of the problem and obtain the following results about MMDS: W[1]-hardness of the problem parameterized by the pathwidth (and thus, treewidth) of the input graph. W[1]-hardness parameterized by k on split graphs. An algorithm running in time 2^𝒪(vc) |V|^𝒪(1), where vc is the size of a minimum-sized vertex cover of the input graph. An ETH-based lower bound showing that the algorithm mentioned in the previous item is optimal.

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02/27/2019

### Algorithm and Hardness results on Liar's Dominating Set and k-tuple Dominating Set

Given a graph G=(V,E), the dominating set problem asks for a minimum sub...
11/07/2022

### Polynomial Kernels for Generalized Domination Problems

In this paper, we study the parameterized complexity of a generalized do...
11/20/2019

### Towards a Theory of Parameterized Streaming Algorithms

Parameterized complexity attempts to give a more fine-grained analysis o...
11/20/2019

### New Algorithms for Mixed Dominating Set

A mixed dominating set is a collection of vertices and edges that domina...
07/13/2021

### Towards exact structural thresholds for parameterized complexity

Parameterized complexity seeks to use input structure to obtain faster a...
01/23/2021

### Exploring the Gap Between Treedepth and Vertex Cover Through Vertex Integrity

For intractable problems on graphs of bounded treewidth, two graph param...
02/05/2019

### Average-case complexity of a branch-and-bound algorithm for min dominating set

The average-case complexity of a branch-and-bound algorithms for Minimum...