Related papers: Covering arrays from maximal sequences over finite…
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…
A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically…
Orientable sequences of order n are infinite periodic sequences with symbols drawn from a finite alphabet of size k with the property that any particular subsequence of length n occurs at most once in a period in either direction. They were…
A universal cycle for a set S of combinatorial objects is a cyclic sequence of length |S|that contains a representation of each element in S exactly once as a substring. If S is the set of k-subsets of [n] = {1, 2, . . . , n}, it is…
After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…
This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach…
A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
The study of strings is an important combinatorial field that precedes the digital computer. Strings can be very long, trillions of letters, so it is important to find compact representations. Here we first survey various forms of one…
Graph construction, a fundamental operation in a data processing pipeline, is typically done by multiplying the incidence array representations of a graph, $\mathbf{E}_\mathrm{in}$ and $\mathbf{E}_\mathrm{out}$, to produce an adjacency…
While Transformers excel in language and vision-where inputs are semantically rich and exhibit univariate dependency structures-their architectural complexity leads to diminishing returns in time series forecasting. Time series data is…
In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On…
The term fractal refers to the fractional dimensions that have recursive nature and exhibit better array factor properties. In this article, we present a new class of sparse array where the recursive nature of a fractal can be used in…
The paper addresses the problem of defining families of ordered sequences $\{x_i\}_{i\in N}$ of elements of a compact subset $X$ of $R^d$ whose prefixes $X_n=\{x_i\}_{i=1}^{n}$, for all orders $n$, have good space-filling properties as…
It has been conjectured that whenever an optimal covering array exists there is also a uniform covering array with the same parameters and this is true for all known optimal covering arrays. When used as a test suite, the application…
Sum-rank-metric codes have wide applications in universal error correction, multishot network coding, space-time coding and the construction of partial-MDS codes for repair in distributed storage. Fundamental properties of sum-rank-metric…
In this paper we devise an optimal construction of fault-tolerant spanners for doubling metrics. Specifically, for any $n$-point doubling metric, any $\eps > 0$, and any integer $0 \le k \le n-2$, our construction provides a…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
It is a classical result that an unrooted tree $T$ having positive real-valued edge lengths and no vertices of degree two can be reconstructed from the induced distance between each pair of leaves. Moreover, if each non-leaf vertex of $T$…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…