相关论文: Synchronization Strings: Efficient and Fast Determ…

The convolution between a text string $S$ of length $N$ and a pattern string $P$ of length $m$ can be computed in $O(N \log m)$ time by FFT. It is known that various types of approximate string matching problems are reducible to…

The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…

We present a reconfiguration analogue of alphabet reduction \`a la Dinur (J. ACM, 2007) and its applications. Given a binary constraint graph $G$ and its two satisfying assignments $\psi^\mathsf{ini}$ and $\psi^\mathsf{tar}$, the Maxmin…

We consider the problem of binary string reconstruction from the multiset of its substring compositions, i.e., referred to as the substring composition multiset, first introduced and studied by Acharya et al. We introduce a new algorithm…

Let $W$ be a string of length $n$ over an alphabet $\Sigma$, $k$ be a positive integer, and $\mathcal{S}$ be a set of length-$k$ substrings of $W$. The ETFS problem asks us to construct a string $X_{\mathrm{ED}}$ such that: (i) no string of…

String-averaging is an algorithmic structure used when handling a family of operators in situations where the algorithm at hand requires to employ the operators in a specific order. Sequential orderings are well-known and a simultaneous…

In the Manhattan Sequence Consensus problem (MSC problem) we are given $k$ integer sequences, each of length $l$, and we are to find an integer sequence $x$ of length $l$ (called a consensus sequence), such that the maximum Manhattan…

A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with…

Contrary to common belief, a recent work by Ellen, Gelashvili, Shavit, and Zhu has shown that computability does not require multicore architectures to support "strong" synchronization instructions like compare-and-swap, as opposed to…

The seminal work of Bencz\'ur and Karger demonstrated cut sparsifiers of near-linear size. Subsequent extensions have yielded sparsifiers for hypergraph cuts and more recently linear codes over Abelian groups. A decade ago, Kogan and…

String matching is a fundamental problem in computer science, with critical applications in text retrieval, bioinformatics, and data analysis. Among the numerous solutions that have emerged for this problem in recent decades,…

Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider…

This paper summarizes several developments in string-derived (Minimal Supersymmetric) Standard Models. Part one reviews the first string model containing solely the three generations of the Minimal Supersymmetric Standard Model and a single…

We study codes that can detect the exact number of deletions and insertions in concatenated binary strings. We construct optimal codes for the case of detecting up to $\del$ deletions. We prove the optimality of these codes by deriving a…

We present an explicit and efficient algebraic construction of capacity-achieving list decodable codes with both constant alphabet and constant list sizes. More specifically, for any $R \in (0,1)$ and $\epsilon>0$, we give an algebraic…

Reed-Solomon codes are a classic family of error-correcting codes consisting of evaluations of low-degree polynomials over a finite field on some sequence of distinct field elements. They are widely known for their optimal unique-decoding…

Little String Theory (LST) is a still somewhat mysterious theory that describes the dynamics near a certain class of time-like singularities in string theory. In this paper we discuss the topological version of LST, which describes…

We study the complexity of the problem of searching for a set of patterns that separate two given sets of strings. This problem has applications in a wide variety of areas, most notably in data mining, computational biology, and in…

The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets…

We study the fundamental problem of finding the best string to represent a given set, in the form of the Closest String problem: Given a set $X \subseteq \Sigma^d$ of $n$ strings, find the string $x^*$ minimizing the radius of the smallest…