Related papers: Metric Distortion Bounds for Randomized Social Cho…
We study the design of one-to-one matching mechanisms that are strategy-proof for both sides and as stable as possible. Motivated by the impossibility result of Roth (1982), we formulate the mechanism design problem as a linear program that…
A Condorcet winning set is a set of candidates such that no other candidate is preferred by at least half the voters over all members of the set. The Condorcet dimension, which is the minimum cardinality of a Condorcet winning set, is known…
In the online matching on the line problem, the task is to match a set of requests $R$ online to a given set of servers $S$. The distance metric between any two points in $R\,\cup\, S$ is a line metric and the objective for the online…
We study approximation algorithms for variants of the \emph{median string} problem, which asks for a string that minimizes the sum of edit distances from a given set of $m$ strings of length $n$. Only the straightforward $2$-approximation…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
The approximation ratio has become one of the dominant measures in mechanism design problems. In light of analysis of algorithms, we define the \emph{smoothed approximation ratio} to compare the performance of the optimal mechanism and a…
We study the facility location games with candidate locations from a mechanism design perspective. Suppose there are n agents located in a metric space whose locations are their private information, and a group of candidate locations for…
We introduce a novel definition for a small set R of k points being "representative" of a larger set in a metric space. Given a set V (e.g., documents or voters) to represent, and a set C of possible representatives, our criterion requires…
In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor…
Given an $n$-point metric space $(M,d)$, {\sc metric $1$-median} asks for a point $p\in M$ minimizing $\sum_{x\in M}\,d(p,x)$. We show that for each computable function $f\colon \mathbb{Z}^+\to\mathbb{Z}^+$ satisfying $f(n)=\omega(1)$, {\sc…
Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a…
We consider the problem of computing the smallest possible distortion for embedding of a given n-point metric space into R^d, where d is fixed (and small). For d=1, it was known that approximating the minimum distortion with a factor better…
We initiate the study of distortion in stable matching. Concretely, we aim to design algorithms that have limited access to the agents' cardinal preferences and compute stable matchings of high quality with respect to some aggregate…
Consider the problem of finding a point in a metric space $(\{1,2,\ldots,n\},d)$ with the minimum average distance to other points. We show that this problem has no deterministic $o(n^{1+1/(h-1)})$-query $(2h-\Omega(1))$-approximation…
Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…
Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…
In an election where $n$ voters rank $m$ candidates, a Condorcet winning set is a committee of $k$ candidates such that for any outside candidate, a majority of voters prefer some committee member. Condorcet's paradox shows that some…
We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
We study the distributed facility location games with candidate locations, where agents on a line are partitioned into groups. Both desirable and obnoxious facility location settings are discussed. In distributed location problems,…