Related papers: Symmetries in Sorting
This work continues the development of an intensional approach to computability initiated in previous work, in which programs and computations, rather than functions, constitute the primary objects of study. In this setting, models of…
Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…
For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present…
It has been observed that machine learning algorithms exhibit biased predictions against certain population groups. To mitigate such bias while achieving comparable accuracy, a promising approach is to introduce surrogate functions of the…
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting $n$ distinct elements in this model. In particular, it…
Sorting is an essential operation in computer science with direct consequences on the performance of large scale data systems, real-time systems, and embedded computation. However, no sorting algorithm is optimal under all distributions of…
This note describes an algorithm for enumerating all the elements in a finite set based on uniformly random sampling from the set. This algorithm can be used for enumeration by fair sampling with quantum annealing. Our algorithm is based on…
We introduce a notion of parity for formal morphisms between invertible objects and use it to prove a corresponding coherence theorem. Parity is conceptually similar to the sign of underlying permutations, but not defined as such. To give…
The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The…
A classification is a surjective mapping from a set of objects to a set of categories. A classification aggregation function aggregates every vector of classifications into a single one. We show that every citizen sovereign and independent…
In this paper, we present a framework based on a simple data structure and parameterized algorithms for the problems of finding items in an unsorted list of linearly ordered items based on their rank (selection) or value (search). As a…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
The automatic composition of web services refers to how services can be used in a complex and aggregate manner, to serve a specific and known functionality. Given a list of services described by the input and output parameters, and a…
The (classical) problem of characterizing and enumerating permutations that can be sorted using two stacks connected in series is still largely open. In the present paper we address a related problem, in which we impose restrictions both on…
It is well known that since the sort/shuffle stage in MapReduce is costly, local aggregation is one important principle to designing efficient algorithms. This short paper represents an attempt to more clearly articulate this design…