Related papers: The fair soup division and approximating numbers
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…
Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate…
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
We give a sketch for an alternative proof of a recent result by J. Tseng.
Some Open Problems Concerning Orthogonal Polynomials.
We consider rational points on the sphere and investigate their equidistribution in shrinking spherical caps. For the two-dimensional sphere, we leverage Hecke operators to obtain a significantly improved small-scale equidistribution bound,…
We present some partial results regarding subadditivity of maximal shifts in finite graded free resolutions.
In this paper we study several variations of the \emph{pancake flipping problem}, which is also well known as the problem of \emph{sorting by prefix reversals}. We consider the variations in the sorting process by adding with prefix…
We study short intervals which contain an ``almost square'', an integer $n$ that can be factored as $n = ab$ with $a$, $b$ close to $\sqrt{n}$. This is related to the problem on distribution of $n^2 \alpha \pmod 1$ and the problem on gaps…
We propose a list of open problems in numerical semigroups.
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.
We explore the following question: Is a decision-making program fair, for some useful definition of fairness? First, we describe how several algorithmic fairness questions can be phrased as program verification problems. Second, we discuss…
The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts,…
In this paper we present 43 new inequalities related to integer part and fractional part.
In this paper, we consider the problem of how to fairly dividing $m$ indivisible chores among $n$ agents. The fairness measure we considered here is the maximin share. The previous best known result is that there always exists a…
Fueled by massive data, important decision making is being automated with the help of algorithms, therefore, fairness in algorithms has become an especially important research topic. In this work, we design new streaming and distributed…
We present a new FPTAS for the Subset Sum Ratio problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to $1$ as possible. Our scheme makes use of exact and approximate…
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for…
In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…