Related papers: Genetic algorithms with permutation-based represen…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
The $(1+(\lambda,\lambda))$ genetic algorithm is a bright example of an evolutionary algorithm which was developed based on the insights from theoretical findings. This algorithm uses crossover, and it was shown to asymptotically outperform…
We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a…
In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…
A number system coding for the permutations generated by cyclic shift is described. The system allows to find the rank of a permutation given how it has been generated, and to determine a permutation given its rank. It defines a code…
We give new lower bounds for $M(n,d)$, for various positive integers $n$ and $d$ with $n>d$, where $M(n,d)$ is the largest number of permutations on $n$ symbols with pairwise Hamming distance at least $d$. Large sets of permutations on $n$…
Genetic algorithms have played an important role in engineering optimization. Traditional GAs treat each gene separately. However, biophysical studies of gene regulatory networks revealed direct associations between different genes. It…
Genome rearrangement has been an active area of research in computational comparative genomics for the last three decades. While initially mostly an interesting algorithmic endeavor, now the practical application by applying rearrangement…
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques. An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
Graph neural networks (GNNs) have been shown promising in improving the efficiency of learning communication policies by leveraging their permutation properties. Nonetheless, existing works design GNNs only for specific wireless policies,…
In many applications of evolutionary algorithms the computational cost of applying operators and storing populations is comparable to the cost of fitness evaluation. Furthermore, by knowing what exactly has changed in an individual by an…
Clustering is a difficult and widely-studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g. Euclidean distance) to…
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…
Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$…