Related papers: Smallest Suffixient Sets: Effectiveness, Resilienc…
An upper dominating set is a minimal dominating set in a graph. In the \textsc{Upper Dominating Set} problem, the goal is to find an upper dominating set of maximum size. We study the complexity of parameterized algorithms for \textsc{Upper…
Complex information needs may involve set-compositional queries using conjunction, disjunction, and exclusion, yet it remains unclear whether current retrieval paradigms genuinely satisfy such constraints or exploit `semantic shortcuts'. We…
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
The exponent of a word is the ratio of its length over its smallest period. The repetitive threshold r(a) of an a-letter alphabet is the smallest rational number for which there exists an infinite word whose finite factors have exponent at…
A locally-optimal structure is a combinatorial structure such as a maximal independent set that cannot be improved by certain (greedy) local moves, even though it may not be globally optimal. It is trivial to construct an independent set in…
We consider the problem of summarizing a multi set of elements in $\{1, 2, \ldots , n\}$ under the constraint that no element appears more than $\ell$ times. The goal is then to answer \emph{rank} queries --- given $i\in\{1, 2, \ldots ,…
A finite subset of the natural numbers is weak-Schreier if $\min S \ge |S|$, strong-Schreier if $\min S>|S|$, and maximal if $\min S = |S|$. Let $M_n$ be the number of weak-Schreier sets with $n$ being the largest element and $(F_n)_{n\geq…
In a projective plane $\Pi _{q}$ (not necessarily Desarguesian) of order $q,$ a point subset $S$ is saturating (or dense) if any point of $\Pi _{q}\setminus S$ is collinear with two points in$~S$. Using probabilistic methods, the following…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…
A predecessor (successor) search finds the largest element $x^-$ smaller than the input string $x$ (the smallest element $x^+$ larger than or equal to $x$, respectively) out of a given set $S$; in this paper, we consider the static case…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
This paper provides several optimizations of the rank-based approach for complementing B\"{u}chi automata. We start with Schewe's theoretically optimal construction and develop a set of techniques for pruning its state space that are key to…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
Synchronization strings are recently introduced by Haeupler and Shahrasbi (STOC 2017) in the study of codes for correcting insertion and deletion errors (insdel codes). They showed that for any parameter $\varepsilon>0$, synchronization…
Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…
We consider the family of $\Phi$-Subset problems, where the input consists of an instance $I$ of size $N$ over a universe $U_I$ of size $n$ and the task is to check whether the universe contains a subset with property $\Phi$ (e.g., $\Phi$…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
We consider document listing on string collections, that is, finding in which strings a given pattern appears. In particular, we focus on repetitive collections: a collection of size $N$ over alphabet $[1,\sigma]$ is composed of $D$ copies…
String attractors [STOC 2018] are combinatorial objects recently introduced to unify all known dictionary compression techniques in a single theory. A set $\Gamma\subseteq [1..n]$ is a $k$-attractor for a string $S\in[1..\sigma]^n$ if and…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…