A Fair and Memory/Time-efficient Hashmap

by   Abolfazl Asudeh, et al.

There is a large amount of work constructing hashmaps to minimize the number of collisions. However, to the best of our knowledge no known hashing technique guarantees group fairness among different groups of items. We are given a set P of n tuples in ā„^d, for a constant dimension d and a set of groups š’¢={š _1,ā€¦, š _k} such that every tuple belongs to a unique group. We formally define the fair hashing problem introducing the notions of single fairness (Pr[h(p)=h(x)| pāˆˆš _i, xāˆˆ P] for every i=1,ā€¦, k), pairwise fairness (Pr[h(p)=h(q)| p,qāˆˆš _i] for every i=1,ā€¦, k), and the well-known collision probability (Pr[h(p)=h(q)| p,qāˆˆ P]). The goal is to construct a hashmap such that the collision probability, the single fairness, and the pairwise fairness are close to 1/m, where m is the number of buckets in the hashmap. We propose two families of algorithms to design fair hashmaps. First, we focus on hashmaps with optimum memory consumption minimizing the unfairness. We model the input tuples as points in ā„^d and the goal is to find the vector w such that the projection of P onto w creates an ordering that is convenient to split to create a fair hashmap. For each projection we design efficient algorithms that find near optimum partitions of exactly (or at most) m buckets. Second, we focus on hashmaps with optimum fairness (0-unfairness), minimizing the memory consumption. We make the important observation that the fair hashmap problem is reduced to the necklace splitting problem. By carefully implementing algorithms for solving the necklace splitting problem, we propose faster algorithms constructing hashmaps with 0-unfairness using 2(m-1) boundary points when k=2 and k(m-1)(4+log_2 (3mn)) boundary points for k>2.


page 1

page 2

page 3

page 4

āˆ™ 08/21/2022

Bipartite Matchings with Group Fairness and Individual Fairness Constraints

We address group as well as individual fairness constraints in matchings...
āˆ™ 01/10/2023

Proportionally Fair Matching with Multiple Groups

The study of fair algorithms has become mainstream in machine learning a...
āˆ™ 08/24/2019

Fairness Warnings and Fair-MAML: Learning Fairly with Minimal Data

In this paper, we advocate for the study of fairness techniques in low d...
āˆ™ 09/02/2023

Approximating Fair k-Min-Sum-Radii in ā„^d

The k-center problem is a classical clustering problem in which one is a...
āˆ™ 07/14/2020

A Pairwise Fair and Community-preserving Approach to k-Center Clustering

Clustering is a foundational problem in machine learning with numerous a...
āˆ™ 05/31/2023

Doubly Constrained Fair Clustering

The remarkable attention which fair clustering has received in the last ...
āˆ™ 06/12/2020

Algorithms and Learning for Fair Portfolio Design

We consider a variation on the classical finance problem of optimal port...

Please sign up or login with your details

Forgot password? Click here to reset