Multiwinner Voting with Fairness Constraints

Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting a committee), or specified types such as political leaning (when selecting a subset of news items), an algorithm that chooses a subset by optimizing a multiwinner voting rule may be unbalanced in its selection -- it may under or over represent a particular gender or political orientation in the examples above. We introduce an algorithmic framework for multiwinner voting problems when there is an additional requirement that the selected subset should be "fair" with respect to a given set of attributes. Our framework provides the flexibility to (1) specify fairness with respect to multiple, non-disjoint attributes (e.g., ethnicity and gender) and (2) specify a score function. We study the computational complexity of this constrained multiwinner voting problem for monotone and submodular score functions and present several approximation algorithms and matching hardness of approximation results for various attribute group structure and types of score functions. We also present simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case.Comment: The conference version of this paper appears in IJCAI-ECAI 201

The Maximum Traveling Salesman Problem with Submodular Rewards

In this paper, we look at the problem of finding the tour of maximum reward on an undirected graph where the reward is a submodular function, that has a curvature of $\kappa$, of the edges in the tour. This problem is known to be NP-hard. We analyze two simple algorithms for finding an approximate solution. Both algorithms require $O(|V|^3)$ oracle calls to the submodular function. The approximation factors are shown to be $\frac{1}{2+\kappa}$ and $\max\set{\frac{2}{3(2+\kappa)},2/3(1-\kappa)}$, respectively; so the second method has better bounds for low values of $\kappa$. We also look at how these algorithms perform for a directed graph and investigate a method to consider edge costs in addition to rewards. The problem has direct applications in monitoring an environment using autonomous mobile sensors where the sensing reward depends on the path taken. We provide simulation results to empirically evaluate the performance of the algorithms.Comment: Extended version of ACC 2013 submission (including p-system greedy bound with curvature

A sample decreasing threshold greedy‑based algorithm for big data summarisation

As the scale of datasets used for big data applications expands rapidly, there have been increased efforts to develop faster algorithms. This paper addresses big data summarisation problems using the submodular maximisation approach and proposes an efficient algorithm for maximising general non-negative submodular objective functions subject to k-extendible system constraints. Leveraging a random sampling process and a decreasing threshold strategy, this work proposes an algorithm, named Sample Decreasing Threshold Greedy (SDTG). The proposed algorithm obtains an expected approximation guarantee of 11+k−ϵ for maximising monotone submodular functions and of k(1+k)2−ϵ in non-monotone cases with expected computational complexity of O(n(1+k)ϵlnrϵ). Here, r is the largest size of feasible solutions, and ϵ∈(0,11+k) is an adjustable designing parameter for the trade-off between the approximation ratio and the computational complexity. The performance of the proposed algorithm is validated and compared with that of benchmark algorithms through experiments with a movie recommendation system based on a real database