The Capacity of Some P\'olya String Models

We study random string-duplication systems, which we call P\'olya string models. These are motivated by DNA storage in living organisms, and certain random mutation processes that affect their genome. Unlike previous works that study the combinatorial capacity of string-duplication systems, or various string statistics, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we study the capacity of noisy string-duplication systems, including the tandem-duplication, end-duplication, and interspersed-duplication systems. Interesting connections are drawn between some systems and the signature of random permutations, as well as to the beta distribution common in population genetics

The Capacity of String-Duplication Systems

It is known that the majority of the human genome consists of duplicated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from duplicated sequences and has mutated to its current form. In this paper, we investigate the possibility of constructing an exponentially large number of sequences from a short initial sequence using simple duplication rules, including those resembling genomic-duplication processes. In other words, our goal is to find the capacity, or the expressive power, of these string-duplication systems. Our results include exact capacities, and bounds on the capacities, of four fundamental string-duplication systems. The study of these fundamental biologically inspired systems is an important step toward modeling and analyzing more complex biological processes

The capacity of string-duplication systems

It is known that the majority of the human genome consists of repeated sequences. Furthermore, it is believed that a significant part of the rest of the genome also originated from repeated sequences and has mutated to its current form. In this paper, we investigate the possibility of constructing an exponentially large number of sequences from a short initial sequence and simple duplication rules, including those resembling genomic duplication processes. In other words, our goal is to find out the capacity, or the expressive power, of these string-duplication systems. Our results include the exact capacities, and bounds on the capacities, of four fundamental string-duplication systems

The capacity of some Pólya string models

We study random string-duplication systems, called Pólya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations

Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors

DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction problem, which is applicable whenever multiple reads of noisy data are available. This strategy is uniquely suited to the medium, which inherently replicates stored data in multiple distinct ways, caused by mutations. We consider noise introduced solely by uniform tandem-duplication, and utilize the relation to constant-weight integer codes in the Manhattan metric. By bounding the intersection of the cross-polytope with hyperplanes, we prove the existence of reconstruction codes with greater capacity than known error-correcting codes, which we can determine analytically for any set of parameters.Comment: 11 pages, 2 figures, Latex; version accepted for publicatio

Flexible Yet Secure De-Duplication Service for Enterprise Data on Cloud Storage

The cloud storage services bring forth infinite storage capacity and flexible access capability to store and share large-scale content. The convenience brought forth has attracted both individual and enterprise users to outsource data service to a cloud provider. As the survey shows 56% of the usages of cloud storage applications are for data back up and up to 68% of data backup are user assets. Enterprise tenants would need to protect their data privacy before uploading them to the cloud and expect a reasonable performance while they try to reduce the operation cost in terms of cloud storage, capacity and I/Os matter as well as systems’ performance, bandwidth and data protection. Thus, enterprise tenants demand secure and economic data storage yet flexible access on their cloud data. In this paper, we propose a secure de-duplication solution for enterprise tenants to leverage the benefits of cloud storage while reducing operation cost and protecting privacy. First, the solution uses a proxy to do flexible group access control which supports secure de-duplication within a group; Second, the solution supports scalable clustering of proxies to support large-scale data access; Third, the solution can be integrated with cloud storage seamlessly. We implemented and tested our solution by integrating it with Dropbox. Secure de-duplication in a group is performed at low data transfer latency and small storage overhead as compared to de-duplication on plaintext

The Tandem Duplication Distance Is NP-Hard

In computational biology, tandem duplication is an important biological phenomenon which can occur either at the genome or at the DNA level. A tandem duplication takes a copy of a genome segment and inserts it right after the segment - this can be represented as the string operation AXB ? AXXB. Tandem exon duplications have been found in many species such as human, fly or worm, and have been largely studied in computational biology. The Tandem Duplication (TD) distance problem we investigate in this paper is defined as follows: given two strings S and T over the same alphabet, compute the smallest sequence of tandem duplications required to convert S to T. The natural question of whether the TD distance can be computed in polynomial time was posed in 2004 by Leupold et al. and had remained open, despite the fact that tandem duplications have received much attention ever since. In this paper, we prove that this problem is NP-hard, settling the 16-year old open problem. We further show that this hardness holds even if all characters of S are distinct. This is known as the exemplar TD distance, which is of special relevance in bioinformatics. One of the tools we develop for the reduction is a new problem called the Cost-Effective Subgraph, for which we obtain W[1]-hardness results that might be of independent interest. We finally show that computing the exemplar TD distance between S and T is fixed-parameter tractable. Our results open the door to many other questions, and we conclude with several open problems

Service discovery using Bloom filters

A protocol to perform service discovery in adhoc networks is introduced in this paper. Attenuated Bloom filters are used to distribute services to nodes in the neighborhood and thus enable local service discovery. The protocol has been implemented in a discrete event simulator to investigate the behavior in case of a multihop mobile ad-hoc network with nodes that all have services to offer. Methods to optimize the used bandwidth, which is a scarce resource in wireless networks, are investigated. Experiments performed with the simulator suggest that the proposed service discovery system enables users to find local services in a multihop ad-hoc network efficiently. The costs for advertising can be kept low, whereas the additional costs for queries set due to so-called false positives are moderate

An Extended Stable Marriage Problem Algorithm for Clone Detection

Code cloning negatively affects industrial software and threatens intellectual property. This paper presents a novel approach to detecting cloned software by using a bijective matching technique. The proposed approach focuses on increasing the range of similarity measures and thus enhancing the precision of the detection. This is achieved by extending a well-known stable-marriage problem (SMP) and demonstrating how matches between code fragments of different files can be expressed. A prototype of the proposed approach is provided using a proper scenario, which shows a noticeable improvement in several features of clone detection such as scalability and accuracy.Comment: 20 pages, 10 figures, 6 table

A Running Time Improvement for Two Thresholds Two Divisors Algorithm

Chunking algorithms play an important role in data de-duplication systems. The Basic Sliding Window (BSW) algorithm is the first prototype of the content-based chunking algorithm which can handle most types of data. The Two Thresholds Two Divisors (TTTD) algorithm was proposed to improve the BSW algorithm in terms of controlling the variations of the chunk-size. In this project, we investigate and compare the BSW algorithm and TTTD algorithm from different factors by a series of systematic experiments. Up to now, no paper conducts these experimental evaluations for these two algorithms. This is the first value of this paper. According to our analyses and the results of experiments, we provide a running time improvement for the TTTD algorithm. Our new solution reduces about 7 % of the total running time and also reduces about 50 % of the large-sized chunks while comparing with the original TTTD algorithm and make average chunk-size closer to the expected chunk-size. These significant results are the second important value of this project