LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

The Approximability and Integrality Gap of Interval Stabbing and Independence Problems

Abstract Motivated by problems such as rectangle stabbing in the plane, we study the minimum hitting set and maximum independent set problems for families of d-intervals and d-union-intervals. We obtain the following: (1) constructions yielding asymptotically tight lower bounds on the integrality gaps of the associated natural linear programming relaxations; (2) an LP-relative dapproximation for the hitting set problem on d-intervals; (3) a proof that the approximation ratios for independent set on families of 2-intervals and 2-union-intervals can be improved to match tight duality gap lower bounds obtained via topological arguments, if one has access to an oracle for a PPAD-complete problem related to finding Borsuk-Ulam fixed-points

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum