DeepAI AI Chat
Log In Sign Up

An Improved Lower Bound for Matroid Intersection Prophet Inequalities

09/12/2022
by   Raghuvansh R. Saxena, et al.
Princeton University
Harvard University
0

We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids. The best-known algorithms achieve a Θ(q)-approximation, even when restricted to instances that are the intersection of q partition matroids, and with i.i.d. Bernoulli random variables. The previous best-known lower bound is Θ(√(q)) due to a simple construction of [Kleinberg-Weinberg STOC 2012] (which uses i.i.d. Bernoulli random variables, and writes the construction as the intersection of partition matroids). We establish an improved lower bound of q^1/2+Ω(1/loglog q) by writing the construction of [Kleinberg-Weinberg STOC 2012] as the intersection of asymptotically fewer partition matroids. We accomplish this via an improved upper bound on the product dimension of a graph with p^p disjoint cliques of size p, using recent techniques developed in [Alon-Alweiss European Journal of Combinatorics 2020].

READ FULL TEXT

page 1

page 2

page 3

page 4

10/10/2019

Construction of Const Dimension Code from Two Parallel Versions of Linkage Construction

According the report [10], the lower bound with the highest score is the...
02/19/2020

Improved Approximate Degree Bounds For k-distinctness

An open problem that is widely regarded as one of the most important in ...
07/23/2019

An upper bound on the dimension of the voting system of the European Union Council under the Lisbon rules

The voting rules of the European Council (EU) under the Treaty of Lisbon...
03/25/2020

Improved lower bound on the dimension of the EU council's voting rules

Kurz and Napel (2015) proved that the voting system of the EU council (b...
03/28/2018

Framework for ETH-tight Algorithms and Lower Bounds in Geometric Intersection Graphs

We give an algorithmic and lower-bound framework that facilitates the co...
04/23/2020

The number of almost perfect nonlinear functions grows exponentially

Almost perfect nonlinear (APN) functions play an important role in the d...
02/10/2021

A better lower bound for Lower-Left Anchored Rectangle Packing

Given any set of points S in the unit square that contains the origin, d...