Related papers: Improved Lower Bounds for Constant GC-Content DNA …
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
We study the construction of $d$-deletion-correcting binary codes by formulating the problem as a Maximum Clique Problem (MCP). In this formulation, vertices represent candidate codewords and edges connect pairs whose longest common…
Representing visual data using compact binary codes is attracting increasing attention as binary codes are used as direct indices into hash table(s) for fast non-exhaustive search. Recent methods show that ranking binary codes using…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
This paper considers the problem of approximate nearest neighbor search in the compressed domain. We introduce polysemous codes, which offer both the distance estimation quality of product quantization and the efficient comparison of binary…
In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs…
We consider static, external memory indexes for exact and approximate versions of the $k$-nearest neighbor ($k$-NN) problem, and show new lower bounds under a standard indivisibility assumption: - Polynomial space indexing schemes for…
Recent years have witnessed extensive attention in binary code learning, a.k.a. hashing, for nearest neighbor search problems. It has been seen that high-dimensional data points can be quantized into binary codes to give an efficient…
DNA codes have many applications, such as in data storage, DNA computing, etc. Good DNA codes have large sizes and satisfy some certain constraints. In this paper, we present a new construction method for reversible DNA codes. We show that…
Gene annotation has traditionally required direct comparison of DNA sequences between an unknown gene and a database of known ones using string comparison methods. However, these methods do not provide useful information when a gene does…
Let G=(V,E) be a finite graph, and f:V->N be any function. The Local Search problem consists in finding a local minimum of the function f on G, that is a vertex v such that f(v) is not larger than the value of f on the neighbors of v in G.…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
In this study, a novel coding scheme called highdensity coding based on high-density codebooks using a genetic local search algorithm is proposed. The high-density codebook maximizes the energy transfer capability by maximizing the ratio of…
The Closest String Problem is an NP-hard problem that aims to find a string that has the minimum distance from all sequences that belong to the given set of strings. Its applications can be found in coding theory, computational biology, and…
The exponential increase in storage demand and low lifespan of data storage devices has resulted in long-term archival and preservation emerging as a critical bottlenecks in data storage. In order to meet this demand, researchers are now…
Protein structure prediction can be shown to be an NP-hard problem; the number of conformations grows exponentially with the number of residues. The native conformations of proteins occupy a very small subset of these, hence an exploratory,…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
String barcoding is a recently introduced technique for genomic-based identification of microorganisms. In this paper we describe the engineering of highly scalable algorithms for robust string barcoding. Our methods enable distinguisher…
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…