Related papers: Achieving Fully Proportional Representation is Eas…
We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their…
We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no…
We study the complexity of winner determination in single-crossing elections under two classic fully proportional representation rules---Chamberlin--Courant's rule and Monroe's rule. Winner determination for these rules is known to be…
We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting…
To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an ``optimal'' subset of alternatives. In this paper, we provide a quantitative analysis of…
We investigate two systems of fully proportional representation suggested by Chamberlin Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination…
We investigate winner determination for two popular proportional representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems. Our study focuses on (nearly) single-peaked resp. single-crossing preferences. We show that for…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We present an almost optimal algorithm for the classic Chamberlin-Courant multiwinner voting rule (CC) on single-peaked preference profiles. Given $n$ voters and $m$ candidates, it runs in almost linear time in the input size, improving the…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
We study the complexity of determining a winning committee under the Chamberlin--Courant voting rule when voters' preferences are single-crossing on a line, or, more generally, on a median graph (this class of graphs includes, e.g., trees…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…