Related papers: Ordering Candidates via Vantage Points

Let $\alpha(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in the $p$-random subset of $\mathbb{F}_q^d$. In this note, we determine the order of magnitude of $\alpha(\mathbb{F}_q^{3},p)$ up to a…

We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this…

In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by $k$. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee $(k+2)/3$. This local…

In a graph whose vertices are assigned integer ranks, a path is well-ranked if the endpoints have distinct ranks or some interior point has a higher rank than the endpoints. A ranking is an assignment of ranks such that all nontrivial paths…

How can $d+k$ vectors in $\mathbb{R}^d$ be arranged so that they are as close to orthogonal as possible? In particular, define $\theta(d,k):=\min_X\max_{x\neq y\in X}|\langle x,y\rangle|$ where the minimum is taken over all collections of…

For a finite set $A\subset \mathbb{R}^d$, let $\Delta(A)$ denote the spread of $A$, which is the ratio of the maximum pairwise distance to the minimum pairwise distance. For a positive integer $n$, let $\gamma_d(n)$ denote the largest…

We study a ranking and selection problem of learning from choice-based feedback with dynamic assortments. In this problem, a company sequentially displays a set of items to a population of customers and collects their choices as feedback.…

For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for…

We are interested in computing $k$ most preferred models of a given d-DNNF circuit $C$, where the preference relation is based on an algebraic structure called a monotone, totally ordered, semigroup $(K, \otimes, <)$. In our setting, every…

We study the following question: for given $d\geq 2$, $n\geq d$ and $k \leq n$, what is the largest value $c(d,n,k)$ such that from any set of $n$ unit vectors in $\mathbb{R}^d$, we may select $k$ vectors with corresponding signs $\pm 1$ so…

In this paper we investigate the top-$k$-selection problem, i.e. determine the largest, second largest, ..., and the $k$-th largest elements, in the dynamic data model. In this model the order of elements evolves dynamically over time. In…

We show that any total preorder on a set with $\binom{n}{2}$ elements coincides with the order on pairwise distances of some point collection of size $n$ in $\mathbb{R}^{n-1}$. For linear orders, a collection of $n$ points in…

We revisit the problem of selecting an item from $n$ choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first…

We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our…

We consider $(\epsilon,\delta)$-PAC maximum-selection and ranking for general probabilistic models whose comparisons probabilities satisfy strong stochastic transitivity and stochastic triangle inequality. Modifying the popular knockout…

Let $\# K$ be a number of integer lattice points contained in a set $K$. In this paper we prove that for each $d\in {\mathbb N}$ there exists a constant $C(d)$ depending on $d$ only, such that for any origin-symmetric convex body $K \subset…

The following optimal stopping problem is considered. The vertices of a graph $G$ are revealed one by one, in a random order, to a selector. He aims to stop this process at a time $t$ that maximizes the expected number of connected…

Let $V$ be a vector space over a field $k, P:V\to k, d\geq 3$. We show the existence of a function $C(r,d)$ such that $rank (P)\leq C(r,d)$ for any field $k,char (k)>d$, a finite-dimensional $k$-vector space $V$ and a polynomial $P:V\to k$…

This paper presents various worst-case results on the positive semidefinite (psd) rank of a nonnegative matrix, primarily in the context of polytopes. We prove that the psd rank of a generic n-dimensional polytope with v vertices is at…

Chv\'{a}tal and Klincsek (1980) gave an $O(n^3)$-time algorithm for the problem of finding a maximum-cardinality convex subset of an arbitrary given set $P$ of $n$ points in the plane. This paper examines a generalization of the problem,…