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Many code families such as low-density parity-check codes, fractional repetition codes, batch codes and private information retrieval codes with low storage overhead rely on the use of combinatorial block designs or derivatives thereof. In…

Combinatorics · Mathematics 2020-05-05 Hoang Dau , Olgica Milenkovic

We study a class of combinatorial designs called Kirkman systems, and we show that infinitely many Kirkman systems are well-distributed in a precise sense. Steiner triple systems of order $n$ can achieve a minimum block sum of $n$. Kirkman…

Combinatorics · Mathematics 2019-06-06 William M. Brummond

Steiner triple systems form one of the most studied classes of combinatorial designs. Configurations, including subsystems, play a central role in the investigation of Steiner triple systems. With sporadic instances of small systems, ad-hoc…

Combinatorics · Mathematics 2021-10-04 Daniel Heinlein , Patric R. J. Östergård

To solve the access-balancing problem in distributed storage systems, we introduce a new combinatorial model, called MinVar model for fractional repetition (FR) codes. Since FR codes are based on graphs or set systems, our MinVar model is…

Information Theory · Computer Science 2020-11-25 Wenjun Yu , Xiande Zhang , Gennian Ge

Distributed systems store data objects redundantly to balance the data access load over multiple nodes. Load balancing performance depends mainly on 1) the level of storage redundancy and 2) the assignment of data objects to storage nodes.…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-12-19 Mehmet Aktas , Emina Soljanin

To facilitate load balancing, distributed systems store data redundantly. We evaluate the load balancing performance of storage schemes in which each object is stored at $d$ different nodes, and each node stores the same number of objects.…

Performance · Computer Science 2021-01-26 Mehmet Fatih Aktas , Amir Behrouzi-Far , Emina Soljanin , Philip Whiting

A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in [1] for exchanging blocks of…

Data Structures and Algorithms · Computer Science 2024-06-24 Jin Sima , Chao Pan , Olgica Milenkovic

Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs. Each pair in such a partition is called a nested design pair…

Combinatorics · Mathematics 2024-10-21 Yeow Meng Chee , Son Hoang Dau , Tuvi Etzion , Han Mao Kiah , Wenqin Zhang

In distributed storage systems built using commodity hardware, it is necessary to have data redundancy in order to ensure system reliability. In such systems, it is also often desirable to be able to quickly repair storage nodes that fail.…

Information Theory · Computer Science 2012-01-24 Joseph C. Koo , John Gill

Redundant storage maintains the performance of distributed systems under various forms of uncertainty. This paper considers the uncertainty in node access and download service. We consider two access models under two download service…

Information Theory · Computer Science 2021-08-09 Pei Peng , Moslem Noori , Emina Soljanin

Emerging optical and virtualization technologies enable the design of more flexible and demand-aware networked systems, in which resources can be optimized toward the actual workload they serve. For example, in a demand-aware datacenter…

Networking and Internet Architecture · Computer Science 2023-08-22 Aleksander Figiel , Janne H. Korhonen , Neil Olver , Stefan Schmid

A distributed storage system (DSS) needs to be efficiently accessible and repairable. Recently, considerable effort has been made towards the latter, while the former is usually not considered, since a trivial solution exists in the form of…

Information Theory · Computer Science 2020-01-16 Lukas Holzbaur , Stanislav Kruglik , Alexey Frolov , Antonia Wachter-Zeh

We examine the problem of allocating a given total storage budget in a distributed storage system for maximum reliability. A source has a single data object that is to be coded and stored over a set of storage nodes; it is allowed to store…

Information Theory · Computer Science 2016-11-15 Derek Leong , Alexandros G. Dimakis , Tracey Ho

We commence the study of domination in the incidence graphs of combinatorial designs. Let $D$ be a combinatorial design and denote by $\gamma(D)$ the domination number of the incidence (Levy) graph of $D$. We obtain a number of results…

Combinatorics · Mathematics 2014-05-15 Felix Goldberg , Deepak Rajendraprasad , Rogers Mathew

Storage allocation affects important performance measures of distributed storage systems. Most previous studies on the storage allocation consider its effect separately either on the success of the data recovery or on the service rate…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-11-17 Moslem Noori , Emina Soljanin , Masoud Ardakani

Distributed storage systems (DSSs) provide a scalable solution for reliably storing massive amounts of data coming from various sources. Heterogeneity of these data sources often means different data classes (types) exist in a DSS, each…

Information Theory · Computer Science 2017-01-24 Koosha Pourtahmasi Roshandeh , Moslem Noori , Masoud Ardakani , Chintha Tellambura

Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…

Soft Condensed Matter · Physics 2025-07-10 Maximilian C. Hübl , Carl P. Goodrich

We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair process that is exact and uncoded, but table-based. These codes were introduced in…

Information Theory · Computer Science 2012-11-19 Oktay Olmez , Aditya Ramamoorthy

The design and implementation of efficient concurrent data structures have seen significant attention. However, most of this work has focused on concurrent data structures providing good \emph{worst-case} guarantees. In real workloads,…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-04 Vitaly Aksenov , Dan Alistarh , Alexandra Drozdova , Amirkeivan Mohtashami

We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the…

Information Theory · Computer Science 2010-10-14 Salim El Rouayheb , Kannan Ramchandran
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