Related papers: A class of orders with linear? time sorting algori…
While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series…
Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…
Sorting is a fundamental algorithmic pre-processing technique which often allows to represent data more compactly and, at the same time, speeds up search queries on it. In this paper, we focus on the well-studied problem of sorting and…
We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…
The need for scalable concurrent ordered set data structures with linearizable range query support is increasing due to the rise of multicore computers, data processing platforms and in-memory databases. This paper presents a new concurrent…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
In this paper, we introduce a new representation for ordered trees, the weight sequence representation. We then use this to construct new representations for both rooted trees and free trees, namely the canonical weight sequence…
The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in $T$.…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
We generalize a well-known algorithm for the generation of all subsets of a set in lexicographic order with respect to the sets as lists of elements (subset-lex order). We obtain algorithms for various combinatorial objects such as the…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
For a renormalizability proof of perturbative models in the Epstein--Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction Lagrangian. This…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…