Related papers: Covering arrays from maximal sequences over finite…
Multivariate time-series forecasting holds immense value across diverse applications, requiring methods to effectively capture complex temporal and inter-variable dynamics. A key challenge lies in uncovering the intrinsic patterns that…
We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of…
The suffix array, perhaps the most important data structure in modern string processing, is often augmented with the longest common prefix (LCP) array which stores the lengths of the LCPs for lexicographically adjacent suffixes of a string.…
In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly…
We provide a deterministic construction of hard instances for the maximum independent set problem (MIS). The constructed hard instances form an infinite graph sequence with increasing size, which possesses similar characteristics to sparse…
Heffter arrays were introduced by Archdeacon in 2015 as an interesting link between combinatorial designs and topological graph theory. Since the initial paper on this topic, there has been a good deal of interest in Heffter arrays as well…
The suffix tree is a very important data structure in string processing, but it suffers from a huge space consumption. In large-scale applications, compressed suffix trees (CSTs) are therefore used instead. A CST consists of three…
We study the fundamental question of how efficiently suffix array entries can be accessed when the array cannot be stored explicitly. The suffix array $SA_T[1..n]$ of a text $T$ of length $n$ encodes the lexicographic order of its suffixes…
We study several variations of line segment covering problem with axis-parallel unit squares in $I\!\!R^2$. A set $S$ of $n$ line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at…
We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their…
This study introduces a novel approach to composite design by employing aperiodic monotiles, shapes that cover surfaces without translational symmetry. Using a combined computational and experimental approach, we study the fracture behavior…
In computer experiments, it has become a standard practice to select the inputs that spread out as uniformly as possible over the design space. The resulting designs are called space-filling designs and they are undoubtedly desirable…
The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a…
Context: Detecting arrays are mathematical structures aimed at fault identification in combinatorial interaction testing. However, they cannot be directly applied to systems that have constraints among test parameters. Such constraints are…
Covering arrays find important application in software and hardware interaction testing. For practical applications it is useful to determine or bound the minimum number of rows, CAN$(t,k,v)$, in a covering array for given values of the…
The correlation properties of sequences form a focal point in the design of multiple access systems of communications. Such a system must be able to serve a number of simultaneous users while keeping interference low. A popular choice for…
The suffix array is a data structure that finds numerous applications in string processing problems for both linguistic texts and biological data. It has been introduced as a memory efficient alternative for suffix trees. The suffix array…
A strong $s$-blocking set in a projective space is a set of points that intersects each codimension-$s$ subspace in a spanning set of the subspace. We present an explicit construction of such sets in a $(k - 1)$-dimensional projective space…
Augmented designs are typically used in early-stage breeding programs to compare single replicates of test entries by combining them with replicated check varieties. One or two dimensional incomplete blocking can be incorporated in the…
An $(r, s)$-formation is a concatenation of $s$ permutations of $r$ letters. If $u$ is a sequence with $r$ distinct letters, then let $\mathit{Ex}(u, n)$ be the maximum length of any $r$-sparse sequence with $n$ distinct letters which has…