Related papers: Circular sorting
This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
A sock ordering is a sequence of socks with different colors. A sock ordering is foot-sortable if the sequence of socks can be sorted by a stack so that socks with the same color form a contiguous block. The problem of deciding whether a…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
Parking sequences (a generalization of parking functions) are defined by specifying car lengths and requiring that a car attempts to park in the first available spot after its preference. If it does not fit there, then a collision occurs…
In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The…
Two planar sets are circularly separable if there exists a circle enclosing one of the sets and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time…
We determine the conditions resulting from equating the area sums of alternative sectors in a circle generated by four, two, and three straight lines, respectively, that connect opposite points on its circumference while passing through a…
The expected number of pairwise comparisons needed to learn a partial order on n elements is shown to be at least n*n/4-o(n*n), and an algorithm is given that needs only n*n/4+o(n*n) comparisons on average. In addition, the optimal strategy…
We propose a framework to assess how to optimally sort and grade students of heterogenous ability. Potential employers face uncertainty regarding an individual's productive value. Knowing which school an individual went to is useful for two…
We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
Clustering is a well-known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. Constrained clustering is a semi-supervised extension to this process that can be…
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…
We arrange the orders in an algebraic number field in a tree. This tree can be used to enumerate all orders of bounded index in the maximal order as well as the orders over some given order.
The note derives an expression for the number of interchanges made by selection sort when the sorting elements are iid variates from geometric distribution. Empirical results reveal we can work with a simpler model compared to what is…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…
It is a long-standing open question to determine the minimum number of comparisons $S(n)$ that suffice to sort an array of $n$ elements. Indeed, before this work $S(n)$ has been known only for $n\leq 22$ with the exception for $n=16$, $17$,…