Related papers: Towards Optimal Sorting of 16 Elements
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…
Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed…
Binary search finds a given element in a sorted array with an optimal number of $\log n$ queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the…
Consider a collection of objects, some of which may be `bad', and a test which determines whether or not a given sub-collection contains no bad objects. The non-adaptive pooling (or group testing) problem involves identifying the bad…
This paper studies the problem of finding the exact ranking from noisy comparisons. A comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly…
Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. That is why a lot of effort has been put into finding sorting algorithms that sort large sets as fast as possible. But the…
We present an extremely simple sorting algorithm. It may look like it is obviously wrong, but we prove that it is in fact correct. We compare it with other simple sorting algorithms, and analyse some of its curious properties.
In preference modelling, it is essential to determine the number of questions and their arrangements to ask from the decision maker. We focus on incomplete pairwise comparison matrices, and provide the optimal filling in patterns, which…
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of $n$ data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences.…
We consider the \emph{approximate minimum selection} problem in presence of \emph{independent random comparison faults}. This problem asks to select one of the smallest $k$ elements in a linearly-ordered collection of $n$ elements by only…
Fair ranking problems arise in many decision-making processes that often necessitate a trade-off between accuracy and fairness. Many existing studies have proposed correction methods such as adding fairness constraints to a ranking model's…
We find large lower bounds for a certain family of algorithms, and prove that such bounds are limited only by natural computability arguments.
We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking,…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…