A Characterization of the Realizable Matoušek Unique Sink Orientations

09/08/2021
by   Simon Weber, et al.
0

The Matoušek LP-type problems were used by Matoušek to show that the Sharir-Welzl algorithm may require at least subexponential time. Later, Gärtner translated this result into the language of Unique Sink Orientations (USOs) and introduced the Matoušek USOs, the USOs equivalent to Matoušek's LP-type problems. He further showed that the Random Facet algorithm only requires quadratic time on the realizable subset of the Matoušek USOs, but without characterizing this subset. In this paper, we deliver this missing characterization and also provide concrete realizations for all realizable Matoušek USOs. Furthermore, we show that the realizable Matoušek USOs are exactly the orientations arising from simple extensions of cyclic-P-matroids.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/20/2020

A New Combinatorial Property of Geometric Unique Sink Orientations

A unique sink orientation (USO) is an orientation of the hypercube graph...
research
04/24/2019

Fast Distributed Algorithms for LP-Type Problems of Bounded Dimension

In this paper we present various distributed algorithms for LP-type prob...
research
02/04/2023

Decompositions of q-Matroids Using Cyclic Flats

We study the direct sum of q-matroids by way of their cyclic flats. Usin...
research
07/13/2022

Realizability Makes a Difference: A Complexity Gap for Sink-Finding in USOs

Algorithms for finding the sink in Unique Sink Orientations (USOs) of th...
research
11/19/2019

Property Testing of LP-Type Problems

Given query access to a set of constraints S, we wish to quickly check i...
research
01/18/2019

Boolean lifting property in quantales

In ring theory, the lifting idempotent property (LIP) is related to some...
research
03/22/2023

Projective positivity of the function systems

The present paper is devoted to the projective positivity in the categor...

Please sign up or login with your details

Forgot password? Click here to reset