Lower Bounds for Dominating Set in Ball Graphs and for Weighted Dominating Set in Unit-Ball Graphs

Mark T. de Berg, Sándor Kisfaludi-Bak

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

1 Citation (Scopus)

Abstract

Recently it was shown that many classic graph problems—Independent Set, Dominating Set, Hamiltonian Cycle, and more—can be solved in subexponential time on unit-ball graphs. More precisely, these problems can be solved in 2O(n1−1/d) time on unit-ball graphs in Rd , which is tight under ETH. The result can be generalized to intersection graphs of similarly-sized fat objects.

For Independent Set the same running time can be achieved for non-similarly-sized fat objects, and for the weighted version of the problem. We show that such generalizations most likely are not possible for Dominating Set: assuming ETH, we prove that
there is no algorithm with running time 2o(n) for Dominating Set on (non-unit) ball graphs in R3 ;

there is no algorithm with running time 2o(n) for Weighted Dominating Set on unit-ball graphs in R3 ;

there is no algorithm with running time 2o(n) for Dominating Set, Connected Dominating Set, or Steiner Tree on intersections graphs of arbitrary convex (but non-constant-complexity) objects in the plane.
Original languageEnglish
Title of host publicationTreewidth, Kernels, and Algorithms
EditorsF. Fomin, S. Kratsch, E. van Leeuwen
Pages31-48
Number of pages18
ISBN (Electronic)978-3-030-42071-0
DOIs
Publication statusPublished - 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12160 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Fingerprint Dive into the research topics of 'Lower Bounds for Dominating Set in Ball Graphs and for Weighted Dominating Set in Unit-Ball Graphs'. Together they form a unique fingerprint.

Cite this